6 Two projectiles, X and Y, are fired into the air from the same place on level ground and reach thesame maximum height, as shown.path of Xgroundpath of YProjectile X is fired vertically upwards and projectile Y is fired at an angle to the horizontal.Air resistance is negligible.Which statement is correct?A X and Y are at rest at their maximum heights.B X and Y are fired with the same speed.C X and Y take the same time to return to the ground.D X and Y travel the same distance.
Question
6 Two projectiles, X and Y, are fired into the air from the same place on level ground and reach thesame maximum height, as shown.path of Xgroundpath of YProjectile X is fired vertically upwards and projectile Y is fired at an angle to the horizontal.Air resistance is negligible.Which statement is correct?A X and Y are at rest at their maximum heights.B X and Y are fired with the same speed.C X and Y take the same time to return to the ground.D X and Y travel the same distance.
Solution
The correct statement is B: X and Y are fired with the same speed.
Here's why:
A) X and Y are at rest at their maximum heights - This is incorrect. At the maximum height, the vertical component of the velocity is zero, but the horizontal component of the velocity for projectile Y is not zero.
B) X and Y are fired with the same speed - This is correct. For both projectiles to reach the same maximum height, they must be launched with the same initial vertical velocity. The initial speed of Y must be greater than X to provide the necessary horizontal component, but the vertical component of Y's velocity must equal X's velocity.
C) X and Y take the same time to return to the ground - This is incorrect. The time of flight depends on the initial velocity and the angle of projection. Since Y is launched at an angle, it will be in the air longer than X.
D) X and Y travel the same distance - This is incorrect. Projectile Y will travel a greater horizontal distance than X, because X is fired vertically and has no horizontal component.
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