a small ball rolls horizontally off the tabletop a small ball rolls horizontally

Question

a small ball rolls horizontally off the tabletop a small ball rolls horizontally off the tabletop a small ball rolls horizontally off the tabletop 1. (a) A car accelerates from rest to 30 m/s in 10 s. Find: (6) its acceleration: (ii) how far it travels While speeding up; (ii) the distance it covers while its velocity changes from 10 m/'s to 20 m/s. (b) A ball is thrown upward with an initial velocity of 12 m/s from a rooftop 40 m high. Find: (0) its velocity on hitting the ground; (ii) the time of flight; (ii) the maximum height. 10 marks

Explanation / Answer

a)

iniital speed , u = 0 m/s

final speed , v = 30 m/s

t = 10 s

i) acceleration = change in velocity/time

acceleration = (30 - 0)/10

acceleration = 3 m/s^2

ii) distance travelled during acceleration = (v^2 - u^2)/2a

distance travelled during acceleration = (30^2 - 0^20)/(2 * 3)

distance travelled during acceleration = 150 m

iii) while travelling from 10 m/s to 20 m/s

distance travelled during acceleration = (v^2 - u^2)/2a

distance travelled during acceleration = (20^2 - 10^20)/(2 * 3)

distance travelled during acceleration = 50 m

b)

u = 12 m/s

h = 40 m

i) Using third equation of motion

v^2 - 12^2 = 2 * 40 * 9.8

v = 30.5 m/s

the final speed is 30.5 m/s

ii)time of flight is t

-40 = 12 * t - 0.50 * 9.8 *t^2

solving for t

t = 4.33 s

the time taken is 4.33 s

iii)

maximum height = 40 + 12^2/(2 * 9.8)

maximum height = 47.3 m

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