Question

A projectile is launched with an initial velocity of
200 meters per second at an angle of 30° above the
horizontal. What is the magnitude of the vertical
component of the projectile's initial velocity by?

(1) 200 m/s x cos 30°
(2) 200 m/s X sin 30°
(3) (200 m/s)/(cos 30 °)
(4) (200 m/s)/(sin 30 °)

Answer 1

i believe the answer is (3)

Answer 2

The magnitude of the vertical component of the projectile's initial velocity is 200 m/s × sin 30°.

The diagrammatic representation of the velocity of the projectile can be seen in the attached image below.

From the diagram, let consider the ΔOAP where Vector OP makes an ∠θ = 30° to the horizontal x-axis.

where;

• |OP| = magnitude of projectile velocity
• |OA| = magnitude of the horizontal component
• |OB|/|AP| = vertical component of the projectile

∴

Using trigonometric approach for ΔOAP;

$\mathbf{sin\theta = \dfrac{AP}{OP}}$

$\mathbf{AP =OP\times sin \theta}}$

AP = 200 × sin 30°

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