To determine the time it takes for the object to reach the ground and the velocity of the object upon striking the ground, we can use the equations of motion for vertical motion under constant acceleration due to gravity.
Let's denote the initial height of the object as h0 (100m), the initial upward velocity as v0 (80m/s), the acceleration due to gravity as g (-9.8m/s^2), the time taken to reach the ground as t, and the final velocity upon striking the ground as vf.
- Time to reach the ground: We can use the equation of motion to determine the time it takes for the object to reach the ground. The equation for the final vertical displacement (h) is:
h = h0 + v0 * t + (1/2) * g * t^2
Since the object is at a height of 100m above the ground initially (h0 = 100m), the final vertical displacement is h = 0 (when it reaches the ground). We can rearrange the equation as follows:
0 = 100 + 80 * t + (1/2) * (-9.8) * t^2
This equation is a quadratic equation in terms of t. We can solve it to find the value of t. In this case, the quadratic equation is:
4.9t^2 + 80t + 100 = 0
By solving this equation, we can find the value of t, which represents the time it takes for the object to reach the ground.
- Velocity upon striking the ground: Once we have determined the time it takes for the object to reach the ground, we can calculate the final velocity upon striking the ground using the equation of motion:
vf = v0 + g * t
By substituting the known values of v0, g, and the calculated value of t, we can find the final velocity vf.
Please note that to solve the quadratic equation and find the exact values of t and vf, you can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 4.9, b = 80, and c = 100. Substitute these values into the quadratic formula to calculate the time t and the final velocity vf.