Question

A projectile is fired from the origin (at y = 0 m) as shown in the diagram. The initial velocity

components are Vox = 310 m/s and Voy = 26 m/s. The projectile reaches maximum
height at point P, then it falls and strikes the ground at point Q, which is 20 m below the launch
point. When the projectile reaches point Q, what is the vertical component of its velocity?
-40 ms
-33 m/s
-26 m/s
-87 m/s
70 m's

Answer 1

The vertical component of the projectile's velocity at point Q is 70 m/s (Option E).

How to calculate the vertical component of the velocity?

The vertical component of the projectile's velocity at point Q is calculated by applying the following formula as shown below;

Vy = Vi + gt

where;

• Vi is the initial vertical component of the velocity
• t is the time of motion
• g is gravity

The time of motion is calculated as;

t = √ (2h/g)

t = √ (2 x 20 / 9.81)

t = 2 s

The time to reach maximum height;

0 = 26 - 9.81t

t = 26 / 9.81

t = 2.6 s

time to return = 2.6 s

Total time = 2.6 s + 2 s

Total time = 4.6 s

Vy = 26 m/s + 9.8 m/s² x 4.6 s

Vy = 71 m/s

Vy ≈ 70 m/s

Answer 2

-26 m/s.

Step-by-step explanation:

Hello,

In this case, since the vertical initial velocity is 26 m/s and the vertical final velocity is 0 m/s at P, we compute the time to reach P:

`t=(0m/s-26m/s)/(-9.8m/s^2) =2.65s`

With which we compute the maximum height:

`y=26m/s*2.65s-(1)/(2)*9.8m/s^2*(2.65s)^2 \\\\y=34.5m`

Therefore, the final velocity until the floor, assuming P as the starting point (Voy=0m/s), turns out:

`v_f=√(0m/s-(-9.8m/s^2)*2*34.5m)\\ \\v_f=-26m/s`

Which is clearly negative since it the projectile is moving downwards the starting point.

Regards.