Answer:

(a)

The vector

makes an angle

with the positive

-axis

The

-component of vector

is

However, we know that the formula for the horizontal component of the vector is

Now,

, then

The magnitude of the velocity vector is

(b) The magnitude of the

-component of the velocity is

Answer:

The false statement is (d) it has constant velocity and changing acceleration.

Acceleration, whether it's changing or constant, always changes the velocity either by changing direction or the magnitude.

Answer:

A particle is said to execute curvilinear motion when it moves in a curved path.

A particle in curvilinear motion has constant horizontal component of velocity. But the vertical velocity component change. Though the magnitude of the velocity remains constant, the direction of the velocity changes. Hence the components of velocity are not equal.

Therefore option (a) is incorrect.

The horizontal and vertical components of velocity are equal only when the angle of projection is

. If the angle of projection is less than that, the horizontal component is greater than the vertical component.

Therefore option (b) is incorrect.

The acceleration and velocity are perpendicular only at the maximum height. At all other points, they are not perpendicular.

Therefore option (d) is incorrect.

The horizontal component of the velocity of the projected object is constant, so the horizontal component of acceleration is zero. The vertical component of the projected object decreases as increase in its height. So, the object has only vertical component of acceleration that is acceleration due to gravity. The acceleration due to gravity has direction along vertical. The direction of velocity of the projectile always changes its direction and magnitude. So, in this situation, the direction of the velocity is non-parallel to the acceleration.

Therefore option (c) is correct.