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A volleyball was hit into the air at a speed of 2020 miles per hour at an angle of 40°40° from the horizontal. Express this velocity in vector form. Round your answer to four decimals.

Question

A volleyball was hit into the air at a speed of 2020 miles per hour at an angle of 40°40° from the horizontal. Express this velocity in vector form. Round your answer to four decimals.

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Solution

To express the velocity in vector form, we need to break it down into its horizontal (x) and vertical (y) components.

The general formulas for these components are:

Vx = V * cos(θ) Vy = V * sin(θ)

where V is the speed of the object, θ is the angle from the horizontal, and Vx and Vy are the horizontal and vertical components of the velocity, respectively.

Given that V = 2020 mph and θ = 40°, we can substitute these values into the formulas:

Vx = 2020 * cos(40°) Vy = 2020 * sin(40°)

Using a calculator, we find:

Vx = 2020 * cos(40°) = 1548.0083 mph (rounded to four decimal places) Vy = 2020 * sin(40°) = 1300.7608 mph (rounded to four decimal places)

So, the velocity of the volleyball in vector form is (1548.0083, 1300.7608).

This problem has been solved

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