Question

If a goat must clear the 4-meter canyon to land on the cliff on the opposite side (assumed to be the same height) and jumps at an angle of 30° to the horizontal, what minimum speed must it have to insure a safe landing? What max height does the goat reach, and how long is the goat in the air?

We haven't used range but we can use it along with equations from velocity, acceleration, vectors etc. I just don't get what steps I'm supposed to use

Answer 1

Let the minimum speed be v

Then the y component of initial velocity is

where theta is 30 degres

horizontal component of initial velocity is

Then the height reached by goat in time t is

When the goat reaches the other side of the cliff, the height is zero

Solving this for t gives

Meanwhile, the horizontal component of velocity remains constant.

Hence the range is

Therefore the minimum speed of the goat is

The maximum height reached is

The goat is in the air for