Question

the angle of launch for a projectile is increased from 55 degrees to 75 degrees. what happens to the range? what happens to the maximum height? a decreases, decreases b increases, decreases c decreases, increases

Explanation:

Step1: Recall range formula

The range formula for projectile motion is \(R=\frac{v_{0}^{2}\sin2\theta}{g}\). When \(\theta = 55^{\circ}\), \(2\theta=110^{\circ}\) and \(\sin110^{\circ}=\sin(180 - 70)^{\circ}=\sin70^{\circ}\approx0.94\). When \(\theta = 75^{\circ}\), \(2\theta = 150^{\circ}\) and \(\sin150^{\circ}=0.5\). Since \(\sin2\theta\) decreases, the range \(R\) decreases.

Step2: Recall maximum - height formula

The maximum - height formula is \(H=\frac{v_{0}^{2}\sin^{2}\theta}{2g}\). When \(\theta = 55^{\circ}\), \(\sin^{2}55^{\circ}\approx(0.82)^{2}=0.67\). When \(\theta = 75^{\circ}\), \(\sin^{2}75^{\circ}\approx(0.97)^{2}=0.94\). Since \(\sin^{2}\theta\) increases, the maximum height \(H\) increases.

Answer:

C. decreases, increases