Question

Assertion The range of a projectile is maximum at 45°

Reason At 0 = 45° , the value of sin theta is maximum


(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false and R is also false.​

Answer 1

Answer:

A is true but R is false

Explanation:

trajectory's range is directly dependant on sin(2θ), there at 45°, sin(2θ) has maximum value i.e. 1.

Answer 2

Concept:

An object is defined as a projectile if it is propelled by the application of an external force and then continues to move freely while being influenced by gravity and air resistance.

Given:

Assertion: The projectile range is greatest at 45 degrees.

Reason: The value of sin theta is greatest when θ = 45°.

Find:

If the Assertion and Reason are true or false.

Solution:

At the top, velocity's vertical component is zero.

Let T be the time it takes to get to the highest point.

Therefore,

$v_y=0=usin\theta -gT$

$T=\frac{usin\theta}{g}$

Therefore, the total time of the flight is:

$=2T\\=\frac{2usin\theta}{g}$

Now, the range is:

$R=ucos\theta \times\frac{2usin\theta}{g}$

$R=\frac{u^2sin2\theta}{g}$

The range is maximum when θ =45°.

Therefore, sin 2θ = sin(90°) = 1

Thus, sin(2θ) has its maximum value at 45°, and as a result, the range is at its maximum.

A is true but R is false.

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