Question

a football was thrown into the air at a speed of 54 miles per hour at an angle of 50° from the horizontal. express this velocity in vector form. round your answer to four decimals.

Explanation:

Step1: Convert speed from miles per hour to a unit - less magnitude (assuming we are just using the magnitude for vector components)

The magnitude of the velocity vector \(v = 54\).

Step2: Find the \(x\) - component of the velocity vector

The formula for the \(x\) - component of a vector \(\vec{v}\) with magnitude \(v\) and angle \(\theta\) (with respect to the horizontal) is \(v_x=v\cos\theta\).
Given \(v = 54\) and \(\theta = 50^{\circ}\), then \(v_x=54\cos(50^{\circ})\).
Using a calculator, \(\cos(50^{\circ})\approx0.6428\), so \(v_x = 54\times0.6428=34.7112\).

Step3: Find the \(y\) - component of the velocity vector

The formula for the \(y\) - component of a vector \(\vec{v}\) with magnitude \(v\) and angle \(\theta\) (with respect to the horizontal) is \(v_y = v\sin\theta\).
Given \(v = 54\) and \(\theta=50^{\circ}\), then \(v_y=54\sin(50^{\circ})\).
Using a calculator, \(\sin(50^{\circ})\approx0.7660\), so \(v_y=54\times0.7660 = 41.3640\).

Answer:

The velocity vector in component form is \(\langle34.7112,41.3640
angle\)