The maximum horizontal range of a rock which is thrown at the same speed but different angles with the horizon and which lands at a level,H,below the initial level occurs when the angle is
A)less than 0 $\circ$
B)0 $\circ$
C)greater than 0 $\circ$ and less than 45 $\circ$ (actual value depends on the value of H)
D)45 $\circ$
E)greater than 45 $\circ$

Question

The maximum horizontal range of a rock which is thrown at the same speed but different angles with the horizon and which lands at a level,H,below the initial level occurs when the angle is
A)less than 0 $\circ$ 
B)0 $\circ$ 
C)greater than 0 $\circ$ and less than 45 $\circ$ (actual value depends on the value of H)
D)45 $\circ$ 
E)greater than 45 $\circ$

Quizplus · Accepted Answer

The maximum range occurs when the projectile is launched at an angle of 45 degrees with respect to the horizontal. However, the question states that the projectile must land at a level below the initial level. This means that the initial vertical velocity must be negative to account for the decrease in height.

Therefore, the optimal angle will depend on the value of H. If H is small, then the optimal angle will be greater than 45 degrees since the projectile must travel a shorter horizontal distance to reach the lower level. If H is large, then the optimal angle will be less than 45 degrees since the projectile must travel a greater horizontal distance to reach the lower level.

Thus, C is the best choice since it accounts for the dependence on the value of H.

The Maximum Horizontal Range of a Rock Which Is Thrown ∘\circ∘

The Maximum Horizontal Range of a Rock Which Is Thrown $\circ$