Question

A ball is thrown horizontally off the edge of a cliff with an initial speed of 20 m/s

. how long does it take for the ball to fall to the ground 86.3 m below?

.How long would it take for the ball to reach the ground 86.3 m below if it were dropped from rest off the cliff edge ?

. how long would it take the ball to fall to the ground 86.3 m below if it were thrown at an initial velocity of 20 m/s but 18° below the horizontal?

Answer 1

The concept behind these types of problems is simple. The motion of any object can be resolved into a horizontal and vertical component. To calculate anything regarding the horizontal/vertical distance or time etc, we can only consider the horizontal/vertical component.

Part 1

The initial vertical component of the velocity is zero. Therefore, the time taken is

Part 2

In this case as well, the initial vertical component of velocity is zero. Therefore, the time taken to reach the bottom is the same as in Part 1.

Part 3

In this case, the initial vertical component is not zero. Since the angle the velocity makes is given with respect to below the horizon, the vertical component is the sine of the angle times the initial velocity.

Since the gravity acts in the same direction as the initial vertical velocity, we get

Putting in our numeric values and rearranging the above equation, we get

Solving this, we get

We actually also get a negative value, which is to be neglected.