Answer:
t = 1.15 + .713 = 1.863 [s]
Explanation:
To solve this problem we must use the following kinematic equation, but first we identify the initial data.
vo = 7 [m/s]
yo = 4 [m]
g = 9.81[m/s^2]
[tex]v_{f}=v_{o}-g*t\\0 = 7 - (9.81*t)\\7 = 9.81*t\\t = 0.713[s][/tex]
The final velocity happens at the moment when the maximum height is reached, at this point the final speed is zero.
[tex]y=y_{o}+v_{o}*t-0.5*g*t^{2}\\ y = 0+ (7*0.713)-0.5*9.81*(0.713)^{2}\\ y = 2.5[m][/tex]
The total elevation will be 2.5 + 4 = 6.5 [m]
Now using again the total height we can find the final velocity.
[tex]v_{f}^2=v_{o}^2+2*g*y\\v_{f}=\sqrt{2*g*y}\\ v_{f}=\sqrt{2*9.81*6.5}\\ v_{f}=11.3[m/s][/tex]
With this final velocity we cand find the time.
[tex]v_{f}=v_{i}+g*t\\11.3=0+9.81*t\\11.3=9.81*t\\t=1.15[s][/tex]
Now we have to sum the two times, the time it takes to go up and the time it takes to go down.
t = 1.15 + .713 = 1.863 [s]
