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Andres kicks a football. Its height in feet is given by h(t)=-16t^(2)+64 t where t represents the time in seconds after kick. After how many seconds does the football hit the ground? Answer: seconds

Andres kicks a football. Its height in feet is given by h(t)=−16t2+64t h(t)=-16 t^{2}+64 t where t t represents the time in seconds after kick. After how many seconds does the football hit the ground?\newlineAnswer: seconds

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Full solution

Q. Andres kicks a football. Its height in feet is given by h(t)=−16t2+64t h(t)=-16 t^{2}+64 t where t t represents the time in seconds after kick. After how many seconds does the football hit the ground?\newlineAnswer: seconds
  1. Set Equation Equal to Zero: To find out when the football hits the ground, we need to solve for tt when h(t)h(t) is equal to 00. The equation given is h(t)=−16t2+64th(t)=-16t^{2}+64t.
  2. Factor Out Common Term: Set the equation equal to zero and solve for tt: 0=−16t2+64t0 = -16t^2 + 64t.
  3. Solve for tt: Factor out the common term, which is 16t16t: 0=16t(−t+4)0 = 16t(-t + 4).
  4. Initial Kick Time: Set each factor equal to zero and solve for tt: 16t=016t = 0 and −t+4=0-t + 4 = 0.
  5. Football Hits Ground: Solving 16t=016t = 0 gives t=0t = 0, which is the time at the initial kick. Solving −t+4=0-t + 4 = 0 gives t=4t = 4 seconds, which is when the football hits the ground.

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