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CALC A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = (2.80 m/s3)t, where the +y-direction is upward. (a) What is the height of the rocket above the surface of the earth at t = 10.0 s? (b) What is the speed of the rocket when it is 325 m above the surface of the earth?
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- A rocket starts from rest and moves upward from What is the height of the rocket above the surface of the earth at t = 10.0 s? the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is (2.80 m/s) t, where the +y- given by ay direction is upward. Express your answer with the appropriate units.arrow_forwardA lunar lander is making its descent to Moon Base I . The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is 5.0 m above the surface and has a downward speed of 0.8 m>s.With the engine off, the lander is in free fall. What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is 1.6 m/s2.arrow_forwardyou wake up in a strange room, and this time you drop a ball from a height of 1.79 m above the floor. The ball hits the floor 0.242 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)? 61.1 m/s^2 30.6 m/s^2 45.9 m/s^2 91.7 m/s^2arrow_forward
- In the vertical jump, an Kobe Bryant starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat Kobe as a particle and let ymax be his maximum height above the floor. Note: this isn't the entire story since Kobe can twist and curl up in the air, but then we can no longer treat him as a particle. Hint: Find v0 to reach y_max in terms of g and y_max and recall the velocity at y_max is zero. Then find v1 to reach y_max/2 with the same kinematic equation. The time to reach y_max is obtained from v0=g (t), and the time to reach y_max/2 is given by v1-v0= -g(t1). Now, t1 is the time to reach y_max/2, and the quantity t-t1 is the time to go from y_max/2 to y_max. You want the ratio of (t-t1)/t1 Note from Asker: I am generally confused on how to manipulate the formulas, so if you could show every step that would be great, Thank You. Part A Part complete To explain why…arrow_forwardYou stand at the edge of a 22.0 m high cliff and throw a stone straight down with a speed of 8.00 m/s. Before it hits the ground, the stone is traveling with a speed of 22.3 m/s. Let down be the positive vertical direction. Using the given coordinate system, what is the sign of the displacement of the stone from the point it is released until just before it hits the ground? O Negative Zero O Positivearrow_forwardThe velocity v of a particle moving in the xy plane is given by v = (6.5t -4.0t2 )i + 6.0j, in m/s. Here v is in m/s and t (for positive time) is in s. What is the acceleration when t = 3.0 s? i-component of acceleration? j-component of acceleration? When (if ever) is the acceleration zero (enter time in s or 'never')? When (if ever) is the velocity zero (enter time in s or 'never')?arrow_forward
- The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 1.54 m above the floor. The ball hits the floor 0.392 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)? 10.0 m/s^2 15.0 m/s^2 30.0 m/s^2 20.0 m/s^2arrow_forwardA diver jumps off a cliff of h at an angle of 0 =38° (see figure below). He reaches a maximum height of hmaz x = 42m from the base of the cliff. Determine the speed of the diver just before he hits the water, = 3m above the top of the cliff before falling to the water below. He hits the water VA =?.Express your answer in units of m/s. Take g 9.80m/s2. Round your answer to zero decimal places. Jrmax Answer:arrow_forwardA toy car starts at rest and accelerates up A 40゚ ramp with acceleration a=(t3)1/2. It then flies into the air, and lands back on the ground. If the height of the ramp is h=6m, What is the horizontal distance X?arrow_forward
- In the vertical jump, an Kobe Bryant starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 ss in the air (their "hang time"). Treat Kobe as a particle and let ymaxymax be his maximum height above the floor. Note: this isn't the entire story since Kobe can twist and curl up in the air, but then we can no longer treat him as a particle. Hint: Find v0 to reach y_max in terms of g and y_max and recall the velocity at y_max is zero. Then find v1 to reach y_max/2 with the same kinematic equation. The time to reach y_max is obtained from v0=g (t), and the time to reach y_max/2 is given by v1-v0= -g(t1). Now, t1 is the time to reach y_max/2, and the quantity t-t1 is the time to go from y_max/2 to y_max. You want the ratio of (t-t1)/t1 To explain why he seems to hang in the air, calculate the ratio of the time he is above ymax/2ymax/2 moving up to the time it takes him to go from the floor to that height. You may ignore…arrow_forwardAn aircraft performs a maneuver called an "aileron roll." During this maneuver, the plane turns like a screw as it maintains a straight flight path, which sets the wings in circular motion. If it takes it 21 s to complete the circle and the wingspan of the plane is 10.6 m, what is the acceleration of the wing tip? Express your answer in m/s².arrow_forwardWhile standing at the edge of the roof of a building, a man throws a stone upward with an initial speed of 6.71 m/s. The stone subsequently falls to the ground, which is 16.7 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: m/s How much time is the stone in the air? elapsed time: Sarrow_forward
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