Determine its speed immediately before landing

[calculator20]

Homework Statement

Please could someone check if I have got this right? Many thanks

The question: An object of mass of 1000kg leaves a 64m high cliff at 100 ms-1 before descending to the ground. Ignoring air resistance, determine its speed immediately before landing.

Homework Equations

I think its a projectiles question using the 'suvat' equations.

The Attempt at a Solution

If I'm ignoring air resistance then I assume that mass is irrelevant?

Vertically I have:

u = 0m/s
v = ?
a = 10m/s2
s = 64m
t = ?

Horizontally I have:

u = 100m/s
v = 100 m/s
a = 0m/s2
s = ?
t = ?


Using the vertical components:

s = ut + 1/2 at^2
so
64 = 0 + 1/2 x 10 x t^2
so
t^2 = (2x64)/10 = 12.8s
t = 3.6s

Then

v = u + at
= 0 + (10x3.6)
= 36m/s

That gives me a horizontal velocity of 100m/s and a vertical velocity of 36m/s which using vector addition (Pythagoras) gives an answer of 106.3m/s.

If someone could tell me if I've got that right that would be great, many thanks!

 

[PhanthomJay]

Well it is best to use conservation of energy methods; the problem doesn't actually state that the object is projected horizontally off the cliff. But no matter, your solution using SUVAT looks good, since the speed will be the same regardless of the projection angle.