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.
Answers
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.
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,
Therefore, the total time of the flight is:
Now, the range is:
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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