Question

A student kicks a soccer ball upward at a 30º angle with an initial speed of 20 m∕s. What expression should the student use to calculate the magnitude of the ball’s initial velocity in the horizontal direction?

Answer 1

`\displaystyle x=10√(3)\ m/s`

`y=10\ m/s`

Step-by-step explanation:

Rectangular coordinates of vectors in 2D

Given a vector with a magnitude v and angle θ with respect to the positive horizontal direction, the x and y components of the vector are given by:

`x=v\cos\theta`

`y=v\sin\theta`

The soccer ball is kicked upward at an angle θ = 30° and at a speed v=20 m/s.

The rectangular components of the vector are:

`x=20\cos 30^\circ`

`\displaystyle x=20\cdot (√(3))/(2)`

Operating:

`\mathbf{\displaystyle x=10√(3)\ m/s}`

`y=20\sin 30^\circ`

`\displaystyle y=20\cdot (1)/(2)`

Operating:

`\mathbf{y=10\ m/s}`