Answer to Question #177260 in Financial Math for daniel wagaye

Question #177260

An object is thrown vertically upward from a height of h0 ft with an initial speed of v0 ft/sec. Its height h (in feet) after t seconds is given by

h= -16t² + v0t + h0. Given this, if it is thrown vertically upward from the ground with an initial speed of 64 ft/sec,

(a) At what time will the height of the ball be 15 ft? (two answers)

(b) How long will it take for the ball to reach 63 ft?


1
Expert's answer
2021-04-15T07:19:59-0400

(a)15=16t2+64t15=-16t^{2}+64t


=16t264t+15=16t^{2}-64t+15


t=b±b24ac2at= \frac {-b± \sqrt{b^2-4ac}}{2a}


t=64±40969602×16t=\frac{64±\sqrt{4096-960}}{2\times16}


t=64+5632=3.75t=\frac{64+56}{32}=3.75


t=645632=0.25t=\frac{64-56}{32}=0.25


3.75 sec and 0.25 sec


(b)63=16tt2+64t63=-16tt^{2}+64t


16t264t+6316t^{2}-64t+63


t=64±409640322×16t=\frac{64± \sqrt{4096-4032}}{2\times16}


t=64+832=2.25t=\frac{64+8 }{32}=2.25


t=64832=1.75t=\frac{64-8}{32}=1.75


2.25 sec

1.75 sec


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