Asked by Jessica

A ball rolls from rest down a smooth ramp that is 16.0m long. The acceleration of the ball is constant at 40ms^2.

A) how long does the ball take to roll the first 4.0m?

B) what is the speed of the ball when it is halfway down the ramp? (how far it has travelled)

C) how long does the ball take to travel the final 8.0m?

Answers

Answered by Damon
d = (1/2) a t^2 = 20 t^2
4 = 20 t^2
t^2 = .2
t = 0.447 seconds
Answered by Damon
8 = 20 t^2
t^2 = 0.4
t = .632
v = a t = 40 ( .632) = 16 m/s
Answered by Jessica
which question is that for
A or C?
Answered by Jessica
What is the final speed of the ball?
Answered by Damon
Vi at 8 m = 16
now accelerates at 40 m/s^2 for 8 more meters
v = Vi + a t = 16 + 40 t
x = Xi + Vi t +20 t^2
16 = 8 + 16 t + 20 t^2
20 t^2 + 16 t - 8 = 0
5 t^2 + 4 t - 2 = 0
t = .348 seconds
Answered by Damon
Hey, it takes awhile :)
by the way
https://www.mathsisfun.com/quadratic-equation-solver.html
Answered by Damon
They did not ask for final speed but I gave you the recipe:
v = Vi + a t = 16 + 40 t
= 16 + 40 ( .348)
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