Question

Which of the curves in the graph below best represent the vertical component Vy of the velocity versus the time t for a projectile fired at an angle of 45 above the horizontal??

Answer 1

D
After projectile is fired, initial vertical component of velocity decreases under retarding force of gravity, becomes stationary momentarily at the maximum height, then increases in the downward (-ve) direction as the projectile falls freely under gravity.

Explanation:

Vertical component of velocity of projectile is given by the kinematic expression

`v=u+at`

In our case

`v_y(t)=v_(y0)-g t`
Acceleration due to gravity `g` is taken as `-ve` as it is in a direction opposite to direction of initial vertical velocity `v_(y0)`.

Rearrange and notice that it represents a straight line. Compare it with standard equation.

`y=mx+c`
`v_y(t)=-g t+v_(y0)`

Slope of the line is negative. Makes an angle greater than `90^@` with `x`-axis.