The initial path of a rocket is 30º above the horizontal,and the horizontal component of the rocket's velocity is 326 m/s.The initial vertical component of the rocket's velocity is
A)188 m/s
B)330 m/s
C)380 m/s
D)280 m/s
E)250 m/s

Question

Quizplus · Accepted Answer

Given that the initial path of the rocket makes an angle of 30º with the horizontal, and the horizontal component of the rocket's velocity is 326 m/s.

Let's assume the initial vertical component of the rocket's velocity as Vv.

So, the horizontal component of the rocket's velocity = Vh = 326 m/s (Given)

The initial path of the rocket makes an angle of 30º with the horizontal. Therefore, we can use trigonometric ratios to find the vertical component of the velocity.

sin 30º = Opposite/Hypotenuse
sin 30º = Vv/Vt   (where Vt is the total velocity)
Vv = Vt sin 30º

Also,
Vt = √[(Vh)^2 + (Vv)^2]  (Pythagoras Theorem)

Substituting Vh and Vv, we get

Vt = √[(326)^2 + (Vv)^2]

Putting this value in the above equation,
Vv = Vt sin 30º
Vv = √[(326)^2 + (Vv)^2] sin 30º

On simplifying,
Vv = 188 m/s

Therefore, the initial vertical component of the rocket's velocity is 188 m/s. Hence, the answer is option A.

The Initial Path of a Rocket Is 30º Above the Horizontal,and