SPRING 2002 #85077

PHYSICS 220A QUIZ 1

1. A sky-diver jumps from the airplane with a speed of 5.6m/s from 115m above the ground, failing to open his parachute. (a) What is his velocity when he falls on the ground? (b) How long is he in the air?

Solution.

(a) We choose downward as positive direction and the jumping position as the origin..

We find the velocity from

              v² = v₀² + 2gh;

              v² = (5.6m/s)² + 2(9.80m/s²)(115m), which gives  v = 47.8m/s

(b) We find the time from

              v = v₀ + gt;

              47.8m/s = 5.6m/s +(9.80m/s²)t, which gives t = 4.3s.

2. A car is traveling from rest, with a varying velocity of v = (3 + 1.5t) m/s, where t is in seconds. Find (a) the distance the car covers in 15s; (b) the car's instantaneous velocity at t = 15s; and (c) the car's instantaneous acceleration at t = 15s.

Solution.

(a) We find the distance from

                x = ò₀^15s(3 + 1.5t)dt = (3t + 1.5/2t²)|₀^15s m = 213.8m.

(b) We find the instantaneous velocity from

               v(1.5s) = [3 + (1.5)(15s)]m/s = 25.5m/s.

(c) We find the instantaneous acceleration from

              a(1.5s) = dv/dt_{t =1.5s} = d(3 + 1.5t)/dt_{t =1.5s} = 1.5m/s².