Warm up problems Problems 3 32 and 3 34 from Knight a A

Last updated: 6/11/2023

Warm up problems Problems 3 32 and 3 34 from Knight a A cannon tilted upward 30 fires a cannonball with a speed of 100 m s What is the component of the cannonball s velocity parallel to the ground about 87 m s b Jack and Jill ran up the hill at 3 0 m s The horizontal component of Jill s velocity vector was 2 5 m s What was the angle of the hill and the vertical component of Jill s velocity 34 1 7 m s Careful measurements have been made of Olympic sprinters in the 100 meter dash A quite realistic model is that the sprinter s velocity is given by v a 1 ebt where t is in 5 v is in m s and the constants a and b are characteristics of the sprinter Sprinter Carl Lewis run at the 87 World Championship is modeled with a 11 81 m s and b 0 6887 s Problem 2 82 from Knight a What was Lewis acceleration at t 0 s 2 00 s and 4 00 s 8 13 2 05 and 0 52 m s b Find an expression for the distance traveled at time t x bt e bt 1 c Your expression from part b is a transcendental equation meaning you can t solve it for t However it is not hard to use trial and error to find the time needed to travel a specific distance To the nearest 0 01 s find the time Lewis needed to sprint 100 0 m His official time was 0 01 s more