A plane moving 200 m/s horizontally fires a projectile with speed 50 m/s in a forward direction 30.0° below the horizontal.At that instant,what is the speed of the projectile with respect to a stationary observer on the ground?
A)245 m/s
B)250 m/s
C)268 m/s
D)293 m/s

Question

Quizplus · Accepted Answer

The speed of the projectile with respect to a stationary observer on the ground can be found by adding the velocity of the plane to the velocity of the projectile. The horizontal component of the projectile's velocity is $200 \, \text{m/s} + 50 \cos(30^\circ)$ and the vertical component is $50 \sin(30^\circ)$ (downwards, but only the magnitude is needed for speed). The resultant speed is the magnitude of the resultant velocity vector, which can be calculated using the Pythagorean theorem. However, since the vertical component does not affect the horizontal speed directly and we are looking for the total speed (not velocity), we focus on the horizontal component. The correct calculation focuses on adding the plane's speed to the horizontal component of the projectile's speed, which gives approximately 245 m/s.

A Plane Moving 200 M/s Horizontally Fires a Projectile with Speed