For an object thrown at 45° to horizontal, the maximum height (H) and horizontal range (R) are related as:
(1) R = 16H
(2) R = 8H
(3) R = 4H
(4) R = 2H

19. A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s², the range of the missile is:
(1) 40 m
(2) 20 m
(3) 60 m
(4) 50 m

20. Velocity of a projectile in its flight:
(1) Remains constant
(2) First decreases, becomes zero and then increases.
(3) First decreases, reaches minimum and then increases.
(4) First increases, reaches maximum and then decreases.

21. At the maximum height of a projectile, the velocity and acceleration are:
(1) Parallel to each other
(2) Antiparallel to each other
(3) Perpendicular to each other
(4) Inclined to each other at 45°

Let's address each part of the multiple-choice questions one by one:

Relationship between Maximum Height (H) and Range (R) for an Object Thrown at 45°:
When a projectile is launched at an angle of 45° to the horizontal, it achieves its maximum range. For such projectiles, the horizontal range R is four times the maximum height H . This is derived from the equations of projectile motion.
The correct answer is: (3) R = 4H

Range of a Missile Fired for Maximum Range:
For a missile fired at an angle of 45° for maximum range, the formula for range R is given by: R = g v 2 sin ( 2 θ ) ​ where v = 20 m/s , θ = 45° , and g = 10 m/s 2 .
Since sin ( 90° ) = 1 , this simplifies to: R = 10 2 0 2 ​ = 40 m
The correct answer is: (1) 40 m

Velocity of a Projectile in its Flight:
As a projectile is launched, its velocity is affected by gravity. Initially, the velocity decreases as it approaches the peak of its trajectory. After reaching the peak, the velocity increases on the way down due to gravity.
The correct answer is: (3) First decreases, reaches minimum and then increases.

Velocity and Acceleration at the Maximum Height of a Projectile:
At the maximum height of a projectile, the vertical component of the velocity is zero, but the horizontal component remains unchanged. Acceleration due to gravity acts downward and is not zero.
Therefore, the velocity vector (horizontal) is perpendicular to the acceleration vector (vertical).
The correct answer is: (3) Perpendicular to each other

Answered by JessicaJessy | 2025-07-06

For an object thrown at 45°, the maximum height and horizontal range relate as R = 4H. When a missile is fired at 20 m/s, the range is 40 m. Additionally, at maximum height, the velocity vector is horizontal and perpendicular to the vertical acceleration vector.
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Answered by JessicaJessy | 2025-08-10