A student with a third floor dormitory window 32 feet off the ground tosses a water balloon straight up in the air with an initial velocity of 16 feet per second. It turns out that the instantaneous velocity of the water balloon is given by the velocity function v(t) = -32t + 16, where v is measured in feet per second and t is measured in seconds.
Let s(t) represent the height of the water balloon above the ground at time t, and note that s is an antiderivative of v. That is, v is the derivative of s: s'(t) = v(t). Find a formula for s(t) that satisfies the initial condition that the balloon is tossed from 32 feet above ground. In other words, make your formula for s satisfy s(0) = 32.
s(t) = _______
At what time does the water balloon reach its maximum height?
t= _______
At what time does the water balloon land?
t = _______
Compute the three differences:
s(1/2) - s(0) =
s(2) - s (1/2) =
s(2) - s(0) =
What do these differences represent?
What is the total vertical distance traveled by the water balloon from the time it is tossed until the time it lands?
Total vertical distance = _______
The graph of the velocity function y = v(t) on the interval [0, 2] is shown below.
What is the total net signed area bounded by y = v(t) and the t-axis on [0, 2]? You can find the answer to this question in two ways: by using your work above, or by using a familiar geometric formula to compute areas of certain relevant regions.
Total net signed area = _______
(1 point) A student with a third floor dormitory window 32 feet off the ground tosses a water bal...
A projectile is launched from ground level with an initial velocity of v 0 feet per second. Neglecting air? resistance, its height in feet t seconds after launch is given by s equals negative 16 t squared plus v 0 t. Find the? time(s) that the projectile will? (a) reach a height of 80 ft and? (b) return to the ground when v 0 is 32 feet per second. ?(a) Find the? time(s) that the projectile will reach a height...
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...
A student throws a water balloon with speed vo from a height h = 1.52 m at an angle θ=39° above the horizontal toward a target on the ground. The target is located a horizontal distance d = 7.5 m from the student's feet. Assume that the balloon moves without air resistance. Use a Cartesian coordinate system with the origin at the balloon's initial position. Part (a) what is the position vector, Rtarget that originates from the balloon's original position and...
A celebrating student throws a water balloon horizontally from a window 50 m above the ground. It hits the ground 60 m from the building without appreciable air resistance. (a) What is the horizontal component of the velocity of the balloon just before it hits the ground? (b) What is the magnitude of the vertical velocity of the balloon just before it hits the ground?
A water balloon is tossed at an angle o = 51° above the horizontal, from a height of 1.50-m above the ground to a target located Ax = 16.0 m away. The target is located on a platform h = 3.2 m above the ground. What must the initial speed of the water balloon be to hit the target? m/s Target Water Balloon V 0 h 1.50 m Дх
2. A water balloon is thrown upward from a window 25 m above the ground and hits the ground 2.95 s later. What's the maximum height above the window that the balloon reaches? a) 3.77 m b) 2.59 m c) 2.21 m d ) 1.82 m e) 1.17 m 400 m 3. A student who can swim with a speed of 2.5 m/s in still water wants to get to the other side of a 400 m wide river whose...
10. (1 point) If h(t) represents the height of an object in feet above ground level at time t and h(t) is given by h(t) = -1672 +13t+3 find the height of the object at the time when the speed is zero. The height of the object is h(t) feet. Answer(s) submitted:
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...
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 point) A water balloon of mass 380 grams is launched with an initial (vertical) velocity of 43 meters per second. Assume air resistance is proportional to velocity with coefficient 5 grams per second, and use 9.81 meters per second squared for the acceleration due to gravity. (a) Find the height of the balloon as a function of time. h(t) = (b) What is the terminal velocity of the balloon? (Enter your answer as a positive velocity.) The terminal velocity...