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PhysicsQ&A LibraryFlg. 4-51 Problem 91.A projectile is launched with an initial speed of 30 m/s at anangle of 60° above the horizontal. What are the (a) magnitude and(b) angle of its velocity 2.0 s after launch, and (c) is the angle aboveor below the horizontal? What are the (d) magnitude and (e) angleof its velocity 5.0 s after launch, and (f) is the angle above or below105the horizontal?Question

Asked Feb 27, 2020

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Step 1

**Given information:**

Initial velocity of the projectile (u) = 30 m/s

The angle at which it is launched (θ) = 60^{0}

Step 2

We can write the components of the velocity as follows:

x-component (u_{x}) = ucos (60) = 15 m/s

y-component (u_{y}) = usin (60) = 25.93 m/s

We know that in projectile motion the x-component of the velocity remains un effected by the gravitational force. But the y-component of the velocity keeps on changing. The y-component of velocity in the varies as follows:

Therefore, the y-component of the velocity in after 2 s is given by:

Step 3

The magnitude of the velocity after 2 s is given by:

The angle of velocity with the horizontal is given by:

Therefore, the velocity vector makes an angle of 22.970 with the horizontal.

Since the angle is +ve we can say that the angle is made above the horizontal.

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