a football was thrown into the air at a speed of 54 miles per hour at an angle of 50° from the horizontal…

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\rangle)