A ball is thrown vertically, from a height h=24.7m, with velocity vi. It lands on the ground after a time interval Δt. Coordinate axes are indicated in the figure. Assume that air resistance is negligible.

a. Enter an expression for Δy in terms of Δt, a, and the vertical component of the initial velocity, vi.

b. Calculate the time, Δt, in seconds, for the case where the ball starts from rest.

c. Return to the general case, vi≠0, and enter an expression for the vertical component of the final velocity, vf ,at the instant of impact with the ground, in terms of vi, a, and Δt.

d. Calculate the value, in meters per second, of vf for the case where the ball is initially at rest.
 

Transcribed Image Text:

h y X h y X

Answer rating: 100% (QA)

a The vertical displacement of the ball Delta y can be expressed as Delta y h 12 a Delta t2 b When the ball starts from rest the initial vertical velocity vi is 0 Using the equation of motion for uniformly accelerated motion Delta y viDelta t 12 a Delta t2 Since vi 0 for this case the equation simplifies to Delta y 12 a Delta t2 Given that Delta y 247 m and a 981 ms acceleration due to gravity we can solve for Delta t 247 12981Delta t2 247 4905Delta t2 Delta t2 2474905 Delta t sqrt2474905 Delta t approx sqrt5 Delta t approx 224 seconds c The final vertical velocity vf can be expressed as vf vi a Delta t ... View the full answer