You drop a ballfrom a height of 2.0 meters...?

Question

You drop a ball from 2.0 meters and it bounces back to height of 1.5 m. What is the ball's speed just as it leaves the ground after the bounce? Please teach me HOW to get to the answer (which is 5.4 m/s cuz i keep getting sqrt(40)

Answer 1

Use the equation: v^2 = vi^2 + 2a(x-xi)

where v is velocity, vi is inital velocity, a is acceleration (-9.8m/s), x is the height, and xi is the intial height (0)

Basically, set-up that equation so that you are comparing a known velocity (at the top of the bounce = 0) with the unknown initial velocity.

0^2 = vi^2 + 2(-9.8)(1.5 - 0)

vi^2 = -2(-9.8)(1.5)

vi^2 = 29.4

vi = 5.4 m/s

Answer 2

Well the easy way to answer this question would be to ignore the part of the question at the start giving you the first height it was dropped from. I'll show both though.

Since after the first bounce it reaches a max height of 1.5 metres we know that the max potential energy due to gravity is mgh where m is the mass of the ball, g is the acceleration due to gravity and h is the .5 metres.

Energy must be conserved so the max kinetic energy ie after the first bounce must be equal to this so (1/2)mv^2 = mgh

Therefore v=sqrt(2gh)

v=5.4222 m/s

The way using the initial height given just uses the fact that since the ball bounced to .75 of the height of the initial height 75% of the kinetic energy is conserved and hence the max velocity after the bounce can be found.

Answer 3

Your dropping height is not required for this calculation.
Ground velocity i.e. initial velocity u = ? (upward)
Final velocity at a height of 1.5 m, v = 0
Acceleration due to gravity, g = -9.81 m/s^2 (downward)
Maximum height, H = 1.5 m (velocity = 0 at maximum height)

We know, v^2 = u^2 + 2gH
So, 0^2 = u^2 +2(-9.81)(1.5)
0 = u^2 - 29.43
u = sqrt(29.43) =

Answer 4

let initial velocity be " u"
final velocity (v) = 0 (as after it reaches 1.5 m height it falls down)
distance covered (s) =1.5 m
acceleration due to gravity =9.8 m /s
v2 _u2 =2gs

0 -u2 = 2 multiplied by 9.8 multiplied by 1.5

u2 =29.4

u=square root of 29.4 ==5.4 m/s