Question

A projectile is fired with an initial velocity of 300 m/s at an angle above the horizontal. If the projectile’s initial horizontal speed is 67 m/s, what is the angle measuring?

Answer 1

To find the projectile's launch angle, use the formula for cosine to divide the horizontal velocity by the initial velocity. Substituting the given values into the formula, the launch angle is calculated to be roughly 77 degrees above the horizontal.

Step-by-step explanation:

The student is asking about how to find the launch angle of a projectile when given its initial velocity and its horizontal speed. This question involves the use of trigonometry to resolve the initial velocity vector into horizontal and vertical components and then to find the angle above the horizontal at which the projectile was fired.

To solve for the angle, we need to use the trigonometric function cosine (cos), since cos(θ) = adjacent/hypotenuse. Here, the adjacent side is the initial horizontal velocity, and the hypotenuse is the initial speed of the projectile. The formula we will use is:

θ = cos-1(vx / v0)

Given that the initial horizontal speed (vx) is 67 m/s, and the initial speed (v0) is 300 m/s, the calculation will be:

θ = cos-1(67 m/s / 300 m/s)

After calculating, we get:

θ ≈ cos-1(0.22333)

θ ≈ 76.96°

Therefore, the projectile was launched at an angle of approximately 77 degrees above the horizontal.