Problem 4: A catapult launches a test rocket vertically upwards from a well, giving the rocket an initial speed of 80 m/sec at ground level. The engines then fire, and the rocket accelerates upward at 4 m/sec² until it reaches an altitude of 1000 m. a) How long does it take the rocket to reach the altitude of 1000 m? Answer: 10 sec b) What is the speed of the rocket when it reaches an altitude of 1000 m? Answer: 120 m/sec Time t y 1000 m. t=0 Yo=0- Vo = 80 m/sec a = 4 m/sec² Engines On Vo ¯†à v = 0 m/sec When the rocket reaches an altitude of 1000 m, the engines fail and the rocket goes into free fall, with an acceleration of a = -g. For the remainder of this problem, the rocket engines will be off. We will re-define t = 0 sec to be the time when the rocket is at an altitude of 1000 m. The initial properties of the rocket will be the properties of the rocket at 1000. c) What is the largest height the rocket reaches? Answer: 1734.7 m d) What is the time it takes the rocket to hit the ground? Answer: 31.06 sec e) What is the velocity of the rocket just before it hits the ground? Answer: -184.4 m/sec AY Engines Off

The drawing shows a skateboarder moving at 6.80 m/s along a horizontal section of a track that is slanted upward by 0 = 41.0° above the horizontal at its end, which is 0.780 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track. 6.80m/s 0.780m

A bowling ball is attached to a 3.73-meter long cable and hung from the ceiling. The cable is kept taut and the ball is raised to an initial height of 1.73 meters above the classroom floor. It is released from rest and allowed to swing as a pendulum. Determine its speed (in m/s) when it is at a height of 1.19 meters above the floor. Answer: m/s (round to the nearest hundredth)

We drop a plastic ball to the floor from a height of 2.0 m and let it bounce several times. 30% of energy is lost with each bounce. How much time passes between the first and second bounce and between the second and third bounce?