Free Projectile Motion MCQs with Answers

1. For a projectile launched from level ground, the maximum range is obtained at a launch angle of

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 90 degrees

Explanation: Range is proportional to sine of twice the launch angle, which is largest when twice the angle is 90 degrees, so the angle itself is 45 degrees. This assumes level ground and no air resistance; in real conditions the optimum drops slightly below 45 degrees. A launch at 90 degrees goes straight up and returns to the starting point with zero range.

2. At the highest point of the path of a projectile, its velocity is

• A. zero in every direction
• B. horizontal only, with the vertical component zero
• C. vertical only
• D. equal to the launch velocity

Explanation: Gravity acts only vertically, so the horizontal component of velocity is unchanged throughout the flight while the vertical component falls to zero at the peak. The projectile is therefore still moving horizontally at the top, which is why its acceleration there is still g downwards even though the vertical velocity is momentarily zero.

3. A projectile launched at angle theta has its maximum range when theta equals

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 90 degrees

Explanation: Range is proportional to sin 2 theta, which is maximum when 2 theta is 90 degrees, that is at 45 degrees, assuming level ground and no air resistance. Angles of 30 and 60 degrees give the same range as each other, since their doubles are supplementary. At 90 degrees the projectile goes straight up and the range is zero.

4. For a projectile in flight, neglecting air resistance, the horizontal component of velocity

• A. increases steadily
• B. decreases steadily
• C. stays constant, because no horizontal force acts
• D. becomes zero at the highest point

Explanation: Gravity acts vertically only, so the horizontal motion is uniform while the vertical motion is uniformly accelerated, and treating the two independently is the key to every projectile problem. At the highest point the vertical component is zero but the horizontal component is unchanged, so the speed there is not zero. This is why a bomb released from a moving aircraft continues to travel forward with it.

5. If the horizontal range of a projectile becomes half of its maximum possible horizontal range, the probable angle of projection is:

• A. 15 degrees
• B. 30 degrees
• C. 45 degrees
• D. 60 degrees

Explanation: Range is proportional to sin of twice the angle and is greatest at 45 degrees, where sin 90 equals 1, so half the maximum range needs sin 2 theta equal to 0.5, giving 2 theta equal to 30 degrees and theta equal to 15 degrees. The other solution is 75 degrees, since the two angles are complementary. Answering 30 degrees comes from halving the angle instead of the sine.

6. A ball is thrown into the air with certain velocity v making an angle with horizontal. If air resistance is neglected, then at maximum height its velocity is:

• A. Equal to initial velocity
• B. Half of initial velocity
• C. Equal to zero
• D. Minimum but not zero

Explanation: At the top the vertical component has fallen to zero, but the horizontal component is unchanged throughout the flight because no horizontal force acts, so the ball still moves horizontally at v cos theta. The speed is therefore at its minimum for the flight yet not zero, which is the distinction being tested. Only a ball thrown straight up would momentarily stop.

7. A projectile is launched in air with certain angle; its velocity is maximum at:

• A. Point of projection
• B. Highest point
• C. Between launching and highest point
• D. At all points

Explanation: The vertical component decreases as the projectile rises and is regained on the way down, so the speed is greatest at launch and again on landing at the same height, and least at the top where only the horizontal component remains. Neglecting air resistance, the landing speed equals the launch speed. This follows directly from energy conservation, since the kinetic energy is greatest where the height is least.