Calculating Free Fall Motion: A Practice Problem with Step-by-Step Solution

[tmc123]

Homework Statement

The original question is:
A ball is shot horizontally off the edge of a cliff 35 m high. The ball lands 20 m from the base of the cliff.
a. How long was the ball in the air?
b. What was the initial velocity of the ball?

Homework Equations

I believe these would be helpful.
x - Δx = vt - (1/2)at^2
x - Δx = Vot + (1/2)at^2

The Attempt at a Solution

To find time, I have this:
20 = 0t - (1/2)(-9.8)t^2
20 = 4.9t^2
t = 2.02 sec

which I then plugged into the second equation to find Vo

20 = Vo (2.02) + (1/2)(-9.8)(2.02)^2
20 = 2.02 Vo - 20
40 = 2.02 Vo
Vo = 19.802 m/s

This unfortunately appears to be in error, but I am unsure where I went astray. I think it's something about the incorrect equations being used, or my not fully understanding the problem.

 

[azizlwl]

The ball is being shot horizontally with certain velocity, not given.
The ball is "dropped" vertically from rest and traveled distance given.
You can find time traveled by the ball to the base.

 

[tmc123]

Hi - just a quick question to clarify. When you say I can find the time by the ball to the base, are you saying that the x is irrelevant (so I should try setting my equation equal to 0 instead of 20?).

 

[azizlwl]

x is the product of time and velocity. No forces acting horizontally, so acceleration is irrelevant.
y is given with initial velocity and acceleration(since there is force acting on it, gravity). From this you can find the time.

 

[tmc123]

Alright. I'll give that a try. Thank you.