Question

A football was thrown into the air at a speed of 57 miles per hour at an angle of 40 from the horizontal, Express this velocity ir vector form. Round your answer tofour decimals.

Answer 1

Given:

the speed of the ball is

`\begin{gathered} v=57\text{ mi/h} \\ v=57*0.4470\text{ m/s} \\ v=25.48\text{ m/s} \end{gathered}`

angle at which the ball is projected

`\theta=40^(\circ)`

Required: the velocity in the vector form

Step-by-step explanation:

look at the diagram below

velocity in the vector form can be written as

`V=v\cos40^(\circ)i+v\sin40^(\circ)j`

here, i and j are unit vectors.

plugging all the value in the above relation, and solve

`\begin{gathered} V=25.48\text{ m/s}*0.7660\text{ }i+25.48\text{ m/s}*0.6428j \\ V=19.5176i+16.3785j \end{gathered}`

final answer is

`\begin{gathered} V=19.5176\imaginaryI+16.3785j\text{ m/s} \\ \lbrack V\rbrack=25.4792\text{ m/s} \end{gathered}`