A toy rocket is launched from the top of a building 144 feet tall at an initial velocity of 231 feet per second. a) Give the function that describes the height of the rocket in terms of time t. b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet. c) For what time interval will the rocket be more than 517 feet above ground level? d) After how many seconds will it hit the ground?
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- A ball is thrown horizontally with a velocity of 5 m/s from the top of a tall cliff. Neglecting air drag, a) What is the speed of the ball 2 seconds later. b) What vertical distance has the ball fallen 2.0 seconds later? You must include a sketch to solveWhile standing on a bridge 13.9 m above the ground, you drop a stone from rest. When the stone has fallen 3.30 m, you throw a second stone straight down. What initial velocity must you give the second stone if they are both to reach the ground at the same instant? Take the downward direction to be the negative direction. Number i UnitsErica throws a lawn dart upward from a height of 1 meter above the ground. The lawn dart reaches a maximum height of 40 m. a) Find the initial velocity of the lawn dart (Answer: 27.6?̂ ? ? ) b) How long after launch does the lawn dart reach its maximum height? (Answer: 2.82 s) c) How long after launch does the lawn dart hit the ground? (Answer: 5.68 ?) d) What is the impact velocity of the lawn dart? (Answer: −28?̂ ? ? ) e) Plot the acceleration vs time and velocity vs time
- A ball is tossed straight up from the ground. If it reaches the height of your bedroom window (2.0 m) and then falls straight back down to the ground, (g= 9.8 m/s?; Ignore air resistance and use at least 2 significant figures.) 1. What was its initial velocity? 2. How long is the ball in the air?A car is traveling at a steady 77 km/h in a 50 km/h zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady 7.2 m/s2 . How much time elapses before the motorcycle is moving as fast as the car? How far is the motorcycle from the car when it reaches this speed?Ahmed and Khalid are having a 100m race from start to finish. Ahmed gives Khalid a 25m head start (he waits until Khalid is 25m away before starting) .Khalid travels at a constant velocity of 5 m/s. Assuming that Ahmed accelerates uniformly from rest at 0.75 m/s2, does he pass Khalid before the finish line? If so, where? If not, how much longer does Khalid take to finish? (explain your reasoning)
- Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a motion diagram, using the particle model, showing the ball’s velocity vectors from the time it is released until it reaches the maximum height on its bounce.Problem 2: Kinematics and vectors. An object is moving on the xy plane with velocities given by: V₂ x = (10.0-0.500t)1 and v = (-5.00t+0.025²) j Determine the following quantities: a. The displacement of the object as a function of time. b. The average velocity of the object from for the time interval from 0 to 10 s.15) You are standing on a cliff 50 m high and throw a rock with an initial velocity of 20 m/s straight up so that the rock eventually lands at the base of the cliff (50 m below you). How long is the rock in the air? a) What is the maximum height of the rock? b) What is the final velocity of the rock? c)
- A scooter begins at rest at t0=0 seconds. The scooters starts moving, and eventually covers a distance d= 651m, in a time tf= 104 seconds. In a coordinate system with north being the positive x-direction, the scooter's motion is in the northern direction. What wa the scooter's average speed, during this time period, in meters per second? What was the scooters displacement in the northern direction during this person, in meters? What was the scooter's average velocity in the northern direction, in this period in meters per second? If the scooter's final velocity at tf was 12 m/s, what was the scooter's average acceleration in the northern direction, during this period in m/s%^2?Standing on the edge of a cliff that is 800 m above the ground. You take a stone and throw it straight up imparting the stone with an initial velocity of 8.30 m/s (UP). What is the velocity of the stone 10 seconds after you throw it up? Air resistance doesn't have an effectA train starts from rest and accelerates uniformly, until it has traveled 5.6 km and acquired a velocity of 42 ms. The train then moves at a constant velocity of 42 m/s for 420 s. The train then slows down uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.6 km of travel is closest to: O 0.20 m/s² O 0.14 m/s² O 0.19 m/s² 0.17 m/s² O 0.16 m/s²