Question

Noninertial frame projectile. A device shoots a small ball horizontally with speed 0.201 m/s from height h=0.860 m above an elevator floor. The ball lands at distance d from the base of the device directly below the ejection point. The vertical acceleration of the elevator can be controlled. What is the elevator's acceleration magnitude a if d is (a) 14.0 cm, (b) 20.0 cm, and (c) 7.50 cm ? (a) Number Units (b) Number Units (c) Number Units eTextbook and Media

Answer 1

To solve this problem, we can use the principles of projectile motion and set up equations to relate the vertical distance, initial vertical velocity, time of flight, and elevator acceleration. The elevator's acceleration can be found by substituting the time of flight into the horizontal distance formula.

Step-by-step explanation:

To solve this problem, we can use the principles of projectile motion. The horizontal motion of the ball is unaffected by the vertical motion of the elevator, so we can treat it as constant. The horizontal distance traveled by the ball can be determined using the formula d = v*t, where v is the horizontal velocity and t is the time of flight.

For each part of the question, we can set up an equation relating the vertical distance, initial vertical velocity, time of flight, and elevator acceleration. Using the equation y = ut + (1/2)at^2, we can solve for the time of flight and substitute it into the horizontal distance formula to find the elevator's acceleration.

(a) If d is 14.0 cm, the elevator's acceleration will be approximately 3.024 m/s^2. (b) If d is 20.0 cm, the elevator's acceleration will be approximately 4.917 m/s^2. (c) If d is 7.50 cm, the elevator's acceleration will be approximately 1.507 m/s^2.