A rocket, initially at rest on the ground, accelerates straight upward with constant net acceleration, B, from time t=0 until t=T1, at which time the fuel is exhausted. Neglect air resistance and assume that the rocket stays close enough to the ground that the acceleration due to gravity (after the rocket engine stops) is given by g. a) Find the maximum height, H, that the rocket reaches above the ground. b) If the rocket's net acceleration, B, is equal to 1.0g, find an expression for the total time, Tmax, that the rocket is in the air (i.e. from liftoff until it hits the ground) in terms of Tı. You do not need to solve your expression numerically but simplify it as much as possible.

Compute your  Average velocity in the following two cases: (a)  You walk 61.4 m at a speed of 2.47 m/s and then run 61.4 m at a speed of 3.34 m/s along a straight track. (B)  You walk for 1 minute at a speed of 2.47 m/s and then run for 1.8 minutes at 3.34 m/s along a straight track

The height of a helicopter above the ground is given by h = 3t^2+2.0t^4, where h is in meters and t is in seconds. At t=2.0s, the helicopter releases a small bag. a) Calculate the maximum height the bag reaches measured from the ground. b) How long after the bad is released, does it strike the ground? c) Calculate the speed of vag when it hits the ground.

A certain freely falling object, released from rest, requires 1.25 s to travel the last 25.0 m before it hits the ground. (a) Find the velocity of the object when it is 25.0 m above the ground. (Indicate the direction with the sign of your answer. Let the positive direction be upward.) m/s (b) Find the total distance the object travels during the fall. m

Objects in free fall on the earth have acceleration ay = -9.8 m/s2. On the moon, free-fall acceleration is approximately 1/6 of the acceleration on earth. This changes the scale of problems involving free fall. For instance, suppose you jump straight upward, leaving the ground with velocity νi and then steadily slowing until reaching zero velocity at your highest point. Because your initial velocity is determined mostly by the strength of your leg muscles, we can assume your initial velocity would be the same on the moon. But considering the final equation in Synthesis 2.1 we can see that, with a smaller free-fall acceleration, your maximum height would be greater. The following questions ask you to think about how certain athletic feats might be performed in this reduced-gravity environment. If an astronaut can jump straight up to a height of 0.50 m on earth, how high could he jump on the moon?A. 1.2 m            B. 3.0 m              C. 3.6 m               D. 18 m

While standing at the edge of the roof of a building, a man throws a stone upward with an initial speed of 5.89 m/s. The stone subsequently falls to the ground, which is 13.1 m below the point where the stone leaves his hand. At what speed does the stone impact the ground? Ignore air resistance and use g = 9.81 m/s2 for the acceleration due to gravity. impact speed: How much time is the stone in the air? elapsed time: m/s

A certain freely falling object, released from rest, requires 1.95 s to travel the last 32.0 m before it hits the ground. (a) Find the velocity of the object when it is 32.0 m above the ground. (Indicate the direction with the sign of your answer. Let the positive direction be upward.) m/s (b) Find the total distance the object travels during the fall. m

3. In Physics, the height of a free-falling object at a given time t is given by h = –16t² + v,t + h., where v, is the initial velocity, and h, is the initial height. A student throws a ball upward from a height of 48ft, initially at 32 ft/s. What is the maximum height of the ball?

A pole vaulter is momentarily motionless as he clears the bar, which is set 4.2 m above the ground. He then falls onto a thick cushion. The top of the cushion is 80 cm above the ground, and it compresses by 50 cm as the pole vaulter comes to rest. What is his acceleration as he comes to rest on the cushion?

rocket, on an unknown planet, launches straight upward. Starting from rest, the rocket accelerates until it reaches 25 m/s then maintains that velocity until its boosters shut off. It eventually falls back to the planet. ASSUME: Starting at t = 0, the rocket accelerates upwards a total distance of 10 m, where it reaches an instantaneous velocity of 25 m/s The moment it reaches an instantaneous velocity of 25 m/s, it travels 30 m upward at a constant speed, then the engines cut off. The moment the engines cut off: the rocket is in free fall From the time it initially launches (t = 0) to the time it lands back on the planet is 7 s The acceleration due to gravity is constant on this planet. HOWEVER you may not assume g = 10 m/s2 Air resistance is negligible DETERMINE: The acceleration due to gravity on this planet