# A man can throw a ball to a maximum horizontal distance of 100 metre. How much high above the ground can be throw the same  ball vertically?

1. 100 metre
2. 200 metre
3. 300 metre
4. 50 metre

## Answer (Detailed Solution Below)

Option 4 : 50 metre
Free
CT 1: हिन्दी (आदिकाल)
7064
10 Questions 40 Marks 10 Mins

## Detailed Solution

Concept:

• Projectile Motion: It is referred to the motion of any object, thrown at an angle from horizontal.  The object is under influence of acceleration due to gravity
• Projectile Motion is an example of a 2-dimensional Motion.

• The horizontal distance covered by an object thrown in such a way is given as:

$$R = \frac{u^{2}sin2θ}{g}$$

• The Maximum Vertical Height obtained by this ball during this motion is given as

$$H = \frac{u^{2}sin^{2}θ}{2g}$$

• The Maximum value a sin function (Sinθ) can obtain is 1

Calculations:

The maximum horizontal range is

$$R = \frac{u^{2}sin2θ}{g}$$

It is maximum when Sin 2θ = 1, then

$$\frac{u^{2}}{g} = 100$$ -- (1)

Given maximum horizontal range = 100 m

Now, the vertical height is given as

$$H = \frac{u^{2}sin^{2}θ}{2g}$$

Its maximum value will be when it is thrown at angle θ = 90 ° that is vertically upward.

Sin 2 θ = 1

Then height is

$$H = \frac{u^{2}}{2g}$$ ---- (2)

Putting (1) in (2) we get

$$H = \frac{u^{2}sin^{2}θ}{2g}$$

$$H = \frac{100}{2} = 50$$

So, the required maximum height is 50m

So, 50m is the correct answer.

Additional Information

• The ball will go to the maximum range when sin 2θ = 90 ° or θ = 45 °
• To get maximum range, any object must be thrown at 45 °
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