Projectile from Height

Question 1:

A ball is thrown horizontally from the top of a 80 m tall building with a speed of 20 m/s. Find the time it takes to reach the ground

1. 4 sec

2. 5 sec

3. 6 sec

4. 7 sec

View Answer

Using formula for Time:

$t = \sqrt{\frac{2h}{g}}$

$t = g 2 h$

$t = \sqrt{\frac{2 \times 80}{10}} = \sqrt{16} = 4 \text{ s}$

$t = 102 \times 80 = 16 = 4 s$

Correct Answer: (1) 4 s

Question 2:

A ball is thrown horizontally with a speed of 20 m/s from a height of 80 m. Find the horizontal distance before hitting the ground.

1. 60 m

2. 70 m

3. 80 m

4. 90 m

View Answer

Using the formula for range in horizontal projectile motion:

$R = v_x \times \sqrt{\frac{2h}{g}}$

$R = v_{x} \times g 2 h$

$R = 20 \times \sqrt{\frac{2 \times 80}{10}}$

$R = 20 \times 102 \times 80$

$R = 20 \times \sqrt{16} = 20 \times 4 = 80 \text{ m}$

$R = 20 \times 16 = 20 \times 4 = 80 m$

Correct Answer: (3) 80 m

Question 3:

A helicopter flying at a height of 125 m and moving horizontally with a speed of 10 m/s drops a package. Find the horizontal distance it covers before hitting the ground.

1. 20 m

2. 30 m

3. 40 m

4. 50 m

View Answer

Using the direct range formula for a projectile dropped from a height:

$R = v_x \times \sqrt{\frac{2h}{g}}$

$R = 10 \times \sqrt{\frac{2 \times 125}{10}}$

$R = 10 \times \sqrt{25} = 10 \times 5 = 50 \text{ m}$

Question 4:

A helicopter is moving horizontally at a constant speed when it drops a package from a certain height. What will be the observed path of the package when viewed from the ground ?

1. A straight vertical line

2. A straight horizontal line

3. A parabola

4. A circle

View Answer

\[ y = -\frac{g}{2 v_x^2} x^2 \]

This is of the form

$y = ax^2$

, which represents a parabolic path. Hence, the object follows a parabolic trajectory when viewed from the ground.

Question 5:

A helicopter is flying horizontally at a constant velocity. It releases a package, which falls freely under gravity. What will be the path of the package as seen by an observer inside the helicopter?

1. A Parabola

2. A Straight line

3. An Ellipse

4. A Circle

View Answer

From the helicopter’s frame of reference, both the helicopter and the package have the same horizontal velocity. Since the package moves downward only due to gravity, it appears to fall straight down in a vertical line when observed from the helicopter.