1: A projectile is launched from the top edge of a cliff of height h. The...
1: A projectile is launched from the top edge of a cliff of height h. The launcher is to deliver a package to some hikers stranded in the valley below. From GPS readings it is known that the hikers are a distance d (known) from the base of the cliff. If the projectile launcher is pointed at an angle θ (known), calculate the speed at which the projectile should be launched.
2: For this problem the heights are low enough that the acceleration due to gravity can be approximated as -g. (Note: even at low Earth orbit, such as the location of the International Space Station, the acceleration due to gravity is not much smaller then g. The apparent weightlessness is due to the space station and its occupants being in free-fall.)
A rocket is launched vertically from a launchpad on the surface of the Earth. The net acceleration (provided by the engines and gravity) is a1 (known) and the burn lasts for t1 seconds (known). Ignoring air resistance calculate:
a) The speed of the rocket at the end of the burn cycle.
b) The height of the rocket when the burn stops.
The main (now empty) fuel tank detaches from the rocket. The rocket is still propelled with the same acceleration as before due to the secondary fuel tank.
c) Calculate how long it takes for the main tank to fall back to the ocean back on the surface of the Earth in order to be recovered for next use.
d) Calculate the height of the rocket at the time when the tank hits the ocean.
e) At the time the main tank hits the ocean the secondary fuel tank runs out of fuel. Calculate the maximum height above the surface of the Earth that is reached by the rocket.
3: a) Consider a vector that points up and to the right at an angle of 45 degrees. Its magnitude is |A|. Write this vector in i-hat, j-hat notation.
b) A vector of similar magnitude points 30 degrees to the left of the positive y axis. Write this vector in i-hat, j-hat notation.
c) A vector of similar magnitude points 12 degrees to the left of the negative y axis. Write this vector in i-hat, j-hat notation.
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1: A projectile is launched from the top edge
of a cliff of height h. The...
2: For this problem the heights are low enough that the acceleration due to gravity can...
2: For this problem the heights are low enough that the acceleration due to gravity can be approximated as -g. (Note: even at low Earth orbit, such as the location of the International Space Station, the acceleration due to gravity is not much smaller then g. The apparent weightlessness is due to the space station and its occupants being in free-fall.) A rocket is launched vertically from a launchpad on the surface of the Earth. The net acceleration (provided by...
A projectile is launched from the top of a cliff at an angle of 45 degrees...
A projectile is launched from the top of a cliff at an angle of 45 degrees and with a velocity of 600 m/s. See Figure 1. What will be the height of the projectile at a distance of 1500 m from the launch point? What will be the distance, d1, from the launch point when the projectile will have a velocity vector at an angle of 60 degrees below the horizontal?
A projectile is fired from the top of a cliff of height h above the ocean...
A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi. (a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height. (b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained by the...
A projectile is fired from the top of a cliff of height h above the ocean...
A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi. (a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height. t = (b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained...
Lab 4: In scenario 3, a projectile is launched from a cliff at some angle above...
Lab 4: In scenario 3, a projectile is launched from a cliff at some angle above horizontal, what are the vector components of the projectile when it reaches its maximum height, above the cliff, before fall back to the earth? A horizontal velocity greater than the initial horizontal velocity at launch. A vertical velocity equal to the initial vertical velocity at launch. A constant horizontal velocity equal to the initial horizontal velocity at launch. A zero vertical velocity, smaller than...
2. A projectile is launched horizontally from a cliff of height of y-50 meters with a...
2. A projectile is launched horizontally from a cliff of height of y-50 meters with a horizontal velocity of v-20/s. a) (5 pts) Draw and label a picture of the problem. b) (10 pts) Determine the time t, that it takes the projectile to hit the ground. d) (10 pts) Determine x, the horizontal distance the projectile has travelled when it hits the ground. d) (10 Pts) Determine the x and y components of the of the projectile's velocity vector...
Please do extra credit 1a. 2. A projectile is launched horizontally from a cliff of height...
Please do extra credit 1a.
2. A projectile is launched horizontally from a cliff of height of y-50 meters with a horizontal velocity of v-20/s. a) (5 pts) Draw and label a picture of the problem. b) (10 pts) Determine the time t, that it takes the projectile to hit the ground. c (10 pts) Determine x, the horizontal distance the projectile has travelled when it hits the ground. d) (10 Pts) Determine the x and y components of the...
[05]= 6.74 and [06]= 2110 13.5. A projectile is launched vertically from the surface of the...
[05]= 6.74 and [06]= 2110
13.5. A projectile is launched vertically from the surface of the earth with an initial speed 0 [05] (a) What is the magnitude of its acceleration (m/s2) [06] surface of the earth? (b) At what height (km) will it stop and begin to fall back to the surface of the earth? km/s. km above the
2 A 5 kg projectile at a height 10 meters was launched at 30 degrees with...
2 A 5 kg projectile at a height 10 meters was launched at 30 degrees with 15 m/s. At the end of the flight, the projectile collided with ground and was thrown up vertically. 2a- Draw the initial and final velocity vectors and measure the earth pulling vector and final velocity direction in digress, provide scale in drawing 2b-- Draw the vector triangle representing the collision of the projectile and ground when the projectile bounced up vertically, provide scale in...
A projectile is launched from the north pole with an initial vertical velocity v_0. What value...
A projectile is launched from the north pole with an initial vertical velocity v_0. What value of v_0 will result in a maximum altitude of 0.61R? Neglect aerodynamic drag and use g = 9.825 m/s^2 as the surface-level acceleration due to gravity and R = 6371 km as the radius of the earth.
2. A projectile is launched horizontally from a cliff of height of y-50 meters with a horizontal velocity of v-20/s. a) (5 pts) Draw and label a picture of the problem. b) (10 pts) Determine the time t, that it takes the projectile to hit the ground. d) (10 pts) Determine x, the horizontal distance the projectile has travelled when it hits the ground. d) (10 Pts) Determine the x and y components of the of the projectile's velocity vector...
Please do extra credit 1a.
2. A projectile is launched horizontally from a cliff of height of y-50 meters with a horizontal velocity of v-20/s. a) (5 pts) Draw and label a picture of the problem. b) (10 pts) Determine the time t, that it takes the projectile to hit the ground. c (10 pts) Determine x, the horizontal distance the projectile has travelled when it hits the ground. d) (10 Pts) Determine the x and y components of the...
[05]= 6.74 and [06]= 2110
13.5. A projectile is launched vertically from the surface of the earth with an initial speed 0 [05] (a) What is the magnitude of its acceleration (m/s2) [06] surface of the earth? (b) At what height (km) will it stop and begin to fall back to the surface of the earth? km/s. km above the
2 A 5 kg projectile at a height 10 meters was launched at 30 degrees with 15 m/s. At the end of the flight, the projectile collided with ground and was thrown up vertically. 2a- Draw the initial and final velocity vectors and measure the earth pulling vector and final velocity direction in digress, provide scale in drawing 2b-- Draw the vector triangle representing the collision of the projectile and ground when the projectile bounced up vertically, provide scale in...
A projectile is launched from the north pole with an initial vertical velocity v_0. What value of v_0 will result in a maximum altitude of 0.61R? Neglect aerodynamic drag and use g = 9.825 m/s^2 as the surface-level acceleration due to gravity and R = 6371 km as the radius of the earth.
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