Question

If a person stands on a bridge 5.0 m above a river and tosses a rock vertically upwards at 10m/s, sailing upwards, reaches its max height, then goes downwards into the river. What is max height of rock and how long does it take to reach max height?

Answer 1

To determine the maximum height reached by the rock and the time it takes to reach that height, we can use the equations of motion for vertical motion under constant acceleration.

Given: Initial velocity ($u$) = 10 m/s (upwards) Acceleration due to gravity ($a$) = -9.8 m/s² (downwards) Height above the river ($s$) = 5.0 m

To find the time ($t$) it takes to reach the maximum height, we can use the following equation:

$v=u+at$

At the maximum height, the final velocity ($v$) will be zero since the rock momentarily comes to a stop before reversing its direction. Therefore:

$0=10-9.8t$

Solving for $t$:

$9.8t=10$

$t=\frac{10}{9.8}$

Now we can find the maximum height ($h$) reached by the rock. We'll use the equation:

$h=ut+\frac{1}{2}a{t}^2$

Substituting the values:

h=10×109.8+12(−9.8)(109.8)2h = 10 imes frac{10}{9.8} + frac{1}{2} (-9.8) left(frac{10}{9.8} ight)^2h=10<spa