Help in Algebra 1. MEDAL

Question

divinesolar · Answer

Question?

calculusxy · Answer

attachment

calculusxy · Answer

I need help in the second part.

faiqraees · Answer

When the height of the object is going to decrease, the velocity is going to increase right?

calculusxy · Answer

The highest point that it can reach is at 2 seconds.

faiqraees · Answer

Since the GPE is being converted into Kinetic energy, the velocity of the object will increase

faiqraees · Answer

Thus the derivative of the function > 0 for the height to decrease

calculusxy · Answer

So what would be the time interval?

welshfella · Answer

after it reaches its maximum height it begins to fall to ground .
The time it takes to fall to groun equals the time it takes to reach maximum height.

faiqraees · Answer

-32t+64> 0 
solve for t

faiqraees · Answer

@welshfella Not necessary. What if the object is thrown from a some distance above the ground and this is true because at t= 0 h = 80

calculusxy · Answer

T = 2

faiqraees · Answer

so t>2 for the object's height to be decreasing

calculusxy · Answer

So it would be 
[2, $\infty$)

faiqraees · Answer

Now they are asking for the reasoning. The reasoning is since it has reached its maximum height, the upward velocity is 0. But since the gravity is still acting on it, it would accelerate towards the earth and thus the distance would decrease

calculusxy · Answer

Thanks @FaiqRaees

welshfella · Answer

yes   thats true

faiqraees · Answer

No problem