y = -16t2 + 68t + 60
y is the ball's height. When it hits the ground, the ball's height is zero. So set y = 0:
0 = -16t2 + 68t + 60
Divide both sides of the equation by -4 to simplify the equation a bit:
0 = 4t2 - 17t - 15
Solve for t using the quadratic formula. Use your calculator to help. You'll get two answers, one positive and one negative. Since we haven't figured out how to go back in time yet, the positive one is the answer. The units are seconds.
San P.
so {x| x = 3/4, 5}
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05/13/21
San P.
Which means that 5 seconds is the right answer! Thank you so much!
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05/13/21
Philip P.
tutor
Some minor quibbles: 1) The variable is t, not x, and 2) the answers are t = -3/4 (not +3/4) and t = 5. The negative answer is going back in time, so t = 5 seconds is the answer. I divided through by -4 to reduce the problem to a simpler quadratic so that the numbers you plugged into the quadratic formula would be smaller and easier to handle. But what you did works.
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05/13/21
San P.
−68±√68^2 - 4(16)(60)/2(-16) => -68 ±√4624+3840/-32 => 68±√8464/-32 => 68±92/-32 so my answers are 3/4 and 5 :)05/13/21