If an object is thrown with a velocity of v feet per second at an angle...
If an object is thrown with a velocity of v feet per second at an angle of θ with the horizontal, then its flight can be modeled by,
x = (v cos θ ) t and y = v (sin θ ) t - 16 t2 + h
where t is in seconds and h is the object's initial height in feet above the ground.
x is the horizontal position and y is the vertical position, and - 16 t2 represents gravity pulling on the object.
Depending on the units involved in the problem, use g = 32 ft/ s2 or g 9.8 m/ s2.
Assume that the ball is hit with an initial velocity of 140 feet per second at an angle of 45° to the horizontal, making contact 3 feet above the ground.
- Find the parametric equations to model the path of the baseball.
- Where is the ball after 2 seconds?
- How long is the ball in the air?
- Is it a home run?
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If an object is thrown with a velocity of v feet per second at
an angle...
Consider a projectile launched at a height h feet above the ground and at an angle θ with the hor...
Consider a projectile launched at a height h feet above the ground and at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = t(v0 cos(θ)) and y = h + (v0 sin(θ))t − 16t2. The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 2 feet above the...
An object is propelled upward at an initial velocity of 32 feet per second at an...
An object is propelled upward at an initial velocity of 32 feet per second at an initial elevation of 48 feet above the ground. The free-fall model used to describe the motion is: s(t) = -1672 + 32t +48 for 03033 (t seconds from release of object). Reference: Drop the Ball Activity The average velocity between t = 2 sec and t = 3 sec A) -48 feet per second B) -24 feet per second C) 16 feet per second...
An object is propelled upward at an initial velocity of 32 feet per second at a....
An object is propelled upward at an initial velocity of 32 feet per second at a. initial elevation of 48 feet above the ground. The free-fall model used to describe the motion is: s(t) = -16t2 + 326 +48 for Osts 3 (t seconds from release of object). Reference: Drop the Ball Activity The average velocity between t = 0 sec and t = 2 sec A) O feet per second B) 24 feet per second C) 12 feet per...
1. If a projectile is fired with an initial velocity of vo meters per second at...
If a projectile is fired with an initial velocity of v0 meters per second at an angle α above the horizontal, and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equationsx=(v0 cos α) t y=(v0 sin α) t-1/2 g t2where g is the acceleration due to gravity (9.8 m / s2)(a) If a projectile is fired with α=45° and v0=900 m / s, when will it hit the ground? How...
A ball is thrown vertically upward with an initial velocity of 48 feet per second.
A ball is thrown vertically upward with an initial velocity of 48 feet per second. The distances (in feet) of the ball from the ground after t seconds is s=48-16t2. (a) At what time t will the ball strike the ground? (b) For what time t is the ball more than 32 feet above the ground?
A ball is thrown vertically upward with an initial velocity of 96 feet per second
A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t)=96t-16t^2a.) at what time will the ball strike the groundb.) for what time t is the ball more than 128 feet above the ground?c.) when will the ball reach its highest peak? how high is it above the ground?
Given information: An object is moving with velocity (in feet per second) described by the function...
Given information: An object is moving with velocity (in feet per second) described by the function v (t) = 4t + 1. We will reason about the object's position function, 8 (t). Question 1 How much does the position change over the time interval (0,4) Answer with a number only (units are feet) 36 Question 2 Question: Think back to the total change theorem. What additional Information would allow us to find a(4), the object's position at time t =...
If a projectile is fired with an initial velocity of vo meters per second at an...
If a projectile is fired with an initial velocity of vo meters per second at an angle a above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = (vo cos(a)t y = (vo sin(a)t - +- 1012 where g is the acceleration due to gravity (9.8 m/s2). (Round your answers to the nearest whole number.) (a) If a gun is fired with a = 30°...
An object is thrown upward at a speed of 161 feet per second by a machine...
An object is thrown upward at a speed of 161 feet per second by a machine from a height of 8 feet off the ground. The height h of the object after t seconds can be found using the equation h(t) = 16t2 + 161t + 8 When will the height be 67 feet? (Write both results, using a comma between). Round answers to the nearest hundredth. Select an answer Select an answer ict reach the ground? seconds 1 answer...
if an object is thrown vertically upward with an initial velocity of v, from an original...
if an object is thrown vertically upward with an initial
velocity of v, from an original position of s, the height h at any
time t is given by:
h = -16t^2 + vt + s
If an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by h16t2 +vt+s (where h and s are in ft, t is in seconds and v...
An object is propelled upward at an initial velocity of 32 feet per second at an initial elevation of 48 feet above the ground. The free-fall model used to describe the motion is: s(t) = -1672 + 32t +48 for 03033 (t seconds from release of object). Reference: Drop the Ball Activity The average velocity between t = 2 sec and t = 3 sec A) -48 feet per second B) -24 feet per second C) 16 feet per second...
An object is propelled upward at an initial velocity of 32 feet per second at a. initial elevation of 48 feet above the ground. The free-fall model used to describe the motion is: s(t) = -16t2 + 326 +48 for Osts 3 (t seconds from release of object). Reference: Drop the Ball Activity The average velocity between t = 0 sec and t = 2 sec A) O feet per second B) 24 feet per second C) 12 feet per...
Given information: An object is moving with velocity (in feet per second) described by the function v (t) = 4t + 1. We will reason about the object's position function, 8 (t). Question 1 How much does the position change over the time interval (0,4) Answer with a number only (units are feet) 36 Question 2 Question: Think back to the total change theorem. What additional Information would allow us to find a(4), the object's position at time t =...
If a projectile is fired with an initial velocity of vo meters per second at an angle a above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = (vo cos(a)t y = (vo sin(a)t - +- 1012 where g is the acceleration due to gravity (9.8 m/s2). (Round your answers to the nearest whole number.) (a) If a gun is fired with a = 30°...
An object is thrown upward at a speed of 161 feet per second by a machine from a height of 8 feet off the ground. The height h of the object after t seconds can be found using the equation h(t) = 16t2 + 161t + 8 When will the height be 67 feet? (Write both results, using a comma between). Round answers to the nearest hundredth. Select an answer Select an answer ict reach the ground? seconds 1 answer...
if an object is thrown vertically upward with an initial
velocity of v, from an original position of s, the height h at any
time t is given by:
h = -16t^2 + vt + s
If an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by h16t2 +vt+s (where h and s are in ft, t is in seconds and v...
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