Question

A cannon launches two projectiles with the same initial speed. Projectile A is launched at 20 degrees above the horizontal. Projectile B is launched at 70 degrees above the horizontal. Which projectile travels a greater horizontal distance?

A) Projectile A
B) Projectile B
C) Both travel the same distance
D) Cannot be determined

Answer 1

Projectile A and Projectile B will travel the same horizontal distance.

Step-by-step explanation:

Projectile A was launched at 20 degrees above the horizontal, while Projectile B was launched at 70 degrees above the horizontal. In projectile motion, horizontal and vertical motions are independent. The horizontal distance traveled by a projectile depends on its initial horizontal velocity and the time of flight, while the vertical distance depends on the initial vertical velocity, the time of flight, and the acceleration due to gravity.

Since Projectile A and Projectile B are launched with the same initial speed, the initial horizontal velocity and the time of flight will be the same for both projectiles. However, the initial vertical velocity will be different due to the difference in launch angles.

When comparing the launch angles of 20 degrees and 70 degrees, the vertical component of the initial velocity for Projectile B will be larger than that of Projectile A. As a result, Projectile B will travel a greater vertical distance. However, since the horizontal distance traveled depends only on the horizontal component of the initial velocity and the time of flight, Projectile A and Projectile B will travel the same horizontal distance.