Show that the initial speed is vi = sqrt 2gL(l-cosθ).

[alevis]

Homework Statement

An object of mass m is suspended from the top of a cart by a string of length L. The cart and object are initially moving to the right at a constant speed vi. The cart comes to rest after colliding and sticking to a bumper, and the suspended object swings through an angle θ.
(a) Show that the initial speed is vi = sqrt 2gL(l-cosθ).
(b) If L = 2.0 m and θ = 40.0°, find the initial speed of the cart.

Homework Equations

KE = PE
1/2mv² = mgh
L1= L-(Lcosθ)

The Attempt at a Solution

1/2mv² = mgh
v² = 2mgh/m
v = sqrt 2gh
stuck!

 

[hage567]

Did you draw a diagram? Look at the situation. How can you express the height the object moves through in terms of the length of the string?