21. A ball is thrown with a slingshot at a velocity of 100 ft/sec. at an angle 2

Question

21. A ball is thrown with a slingshot at a velocity of 100 ft/sec. at an angle 21 above the ground point) from a height of 5 ft. Approximately how long does it take for the ball to hit the ground? Acceleration due to gravity is 32 ft/s2. O 5.83 seconds O 5.89 seconds O2 24 seconds 02.37 seconds 22. Note: Remember to show all af the steps that you use to solve the problem. Be sure to use the (2 point text box where the question mark first appears to show our mathematical work. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answ A shot put is thrown u with a velocity of 35 ft/sec. at a height of 4 ft and an angle of 40%. How long will it take for the shot put to be a horizontal distance of 40 ft. from the person throwing it? Acceleration due to gravity is 32 ft/s Round your answer to the nearest hundredth. Common Symbolsl Templates Geom

Explanation / Answer

Since distance is given in feet, the equation of motion is

y''(t) = 32.

The initial speed =100 ft/s.

The vertical component of the initial velocity is then

y'(0) = 100 sin(21°) 0.836 x 100 ft/s=83.6 ft/s . Integration then gives us

y (t) = 32t + 83.6

The initial height is y(0) = 5 ft, so another integration gives us

y(t) = 16t2 83.6t + 5 ft.

The horizontal component of motion is determined from x(t) = 0 with initial velocity

x(0) = 100 cos(21o) -54.7 ft/s

and initial position x(0) = 0. Integrations give us

x'(t) = -54.7 ft/s and x(t) = -54.7t ft. Summarizing, we have

x(t) = -54.7t, y (t) = 32t + 83.6

32t = 83.6

t = 2.6 hence ball would take approx 2.37 sec to hit the ground

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