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To find the maximum height of the toy rocket when it explodes, we need to first find the time it takes for the rocket to reach its maximum height.
At the maximum height, the velocity of the rocket will be 0. So we can use the formula v = at + v where a = -9.8 m/s^2 and v = 19.6 m/s to solve for the time it takes to reach the maximum height.
0 = -9.8t + 19.6
9.8t = 19.6
t = 2 seconds
Now that we have the time it takes to reach the maximum height, we can use the equation h(t) = 1/2at^2 + vt + s to find the height at t = 2 seconds.
h(2) = 1/2(-9.8)(2)^2 + (19.6)(2) + 0.5
h(2) = -19.6 + 39.2 + 1
h(2) = 20.6 meters
Therefore, the toy rocket is 20.6 meters above the ground when it explodes.