Question

A track & field jumper goes into the long jump with a speed of 5.0 m/s at an angle of 20⁰ above the horizontal. what is the jumper's horizontal speed as they jump? what is their vertical speed?

Answer 1

Answer: Horizontal Speed = 4.6 m/s

Vertical Speed = 1.7 m/s

Step-by-step explanation:

Jumper's velocity = 5 m/s

Angle = 20 degrees

the angle is theta, so theta = 20 degrees

Theta is the angle between the hypothenuse and the adjacent side.

The horizontal side will be the adjacent side, and the vertical side will be the opposite side.

The hypothenuse = 5 m/s

First, let's calculate the adjacent side (horizontal speed)

We have cosine of theta, which is equal to adjacent side / hypothenuse

So,
`cos(20) = adjacent/5`

Multiply 5 on both sides, to get the 5 on the right side canceled.

5cos(20) = adjacent side.

4.6 = adjacent side

Horizontal Speed = 4.6 m/s

Now, let's calculate the vertical speed.

To do that, we need to calculate the opposite side.

We can calculate the opposite side with the help of sin.

The sin of theta equals to opposite side / hypothenuse

`sin(20)=opposite/5`

We do the same thing, multiply 5 on both sides.

5sin(20) = opposite

1.7 = opposite

Vertical Speed = 1.7 m/s

Hope I Helped!