Question

A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in (Figure 1). The ball's position is shown at 1.0 s intervals until t = 3.0 s.At t = 1.0 s the ball's velocity has components vx = 1.0 m/s , vy = 2.5 m/s .

a) Determine the x- and y-components of the ball's velocity at t = 0.0 s.

b) Determine the x- and y-components of the ball's velocity at t = 2.0 s.

c) Determine the x- and y-components of the ball's velocity at t = 3.0 s.

d) What is the value of g on Planet Exidor?

Answer 1

Model: Assume the particle model for the ball, and apply the constant-acceleration kinematic equations of motion in a plane Visualize: Pictorial representation Known x2-y2-t2 vir = 1.0m/s ly 2.5m/s Find Vox Oy Solve: (a) We know the velocity (1.0i+ 2.5j) m/s at t-1s. The ball is at its highest point at t-2 s, so Vy-0 m/s. The horizontal velocity is constant in projectile motion, so vx= 1.0 m/s at all times. Thus = 10/ m/s at t=2 s. We can see that the尸component of velocity changed by ΔⅤ,--25 m/s between t-1s and 2s. Because a, is constant, Vy changes by-25 m/s in any 1-s interval. At t-3 s, v, is 2.5 m/s less than its value of 0 at t-2 s. At t-0s, v must have been 2.5 m/s more than its value of 2.5 m/s at t-1 s. Consequently, at t-0 s, Vo (1.0+50 j) m/s Att=1s, At t 2 s, At t 3s, 7(1) = (1.01+ 2.5) m/S 7(2) = (1.0i + 0.0j) m/s V(3) (1.01 -2.5) m/s (b) Because v is changing at the rate - 2.5m/s per s, the y-component of acceleration is ay--2.5 m/s. But a, -g for projectile motion, so the value of gon Exidor is g-250m/S

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