You’ve taken components of displacement vectors and force vectors. In just the s

Question

You’ve taken components of displacement vectors and force vectors. In just the same way, you can find the components of a velocity vector or an acceleration vector. Given a speed (which is the magnitude of the velocity) and a direction, you can find x and y components of the velocity. The x-component represents how fast you’re moving in the x direction and the y component represents how fast your moving in the y direction. Suppose you kick a ball. Just after it leaves your foot, it is traveling at a velocity of v=22.6 m/s at an angle =29.4°. What is the x component of the velocity just after the ball leaves your foot? What is the y component of the velocity just after the ball leaves your foot? As with other vectors, if you know the components of a velocity vector, you can reconstruct the whole vector. So if you know the horizontal and vertical components of the ball at some other point in its trajectory (path), you can figure out how fast it is traveling at that moment and in what direction. A little while after leaving your foot, you measure the x component of the velocity to be 19.7 m/s and the y component of the velocity to be 6.33 m/s. How fast is the ball traveling (what is its speed) at that point in time? (Remember that speed is the magnitude of the velocity. How do you find the magnitude of a vector given its components?)

Explanation / Answer

vx = 22.6cos29.4 = 19.69 m/s

vy = 22.6sin29.4 = 11.09 m/s

horizontal velocity will be same = vx = 19.7 (always)

in vertical, v_y = vy + at

v_y = 11.09 - 9.81t

v_y = 6.33 m/s

so 6.33 = 11.09 - 9.81t

t = 0.485 sec

and velocity vector is v = v_x i + v_y j

so magnitude Or speed = sqrt[ v_x^2 + v_y^2 ]

for that moment, speed = sqrt[19.7^2 + 6.33^2] = 20.69 m/s

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