Projectile Motion Problem: Finding the Height of a Fence (Intro Physics)

[willworkforfood]

The question I am working from (Intro physics)

"A golf ball is hit at ground level. The ball is observed to reach a maximum height above ground level 8.2 seconds after being hit. 0.6 seconds after reaching its maximum height, the ball is observed to barely clear a fence that is 800ft from where it was hit. The acceleration of gravity is 32 ft/s^2.

How high is the fence in feet?"

Now on to my questions:

1)No initial velocity is given, so can I assume that the initial velocity in the y-direction is 0?

2)How can I solve for the missing time that it takes the ball to clear the fence itself from t=8.8 seconds when it reaches the top of the fence?

I'm not looking for answers or for anyone to work the problem for me, only answers to those questions.

 

[StatusX]

1) it's not 0, but you don't need to know it to solve this problem.
2) say what?

From the time it takes to reach the top you can get the height it ascends to, and then you can figure out how much it falls over the next 0.6 seconds.

 

[HallsofIvy]

The question I am working from (Intro physics)

"A golf ball is hit at ground level. The ball is observed to reach a maximum height above ground level 8.2 seconds after being hit. 0.6 seconds after reaching its maximum height, the ball is observed to barely clear a fence that is 800ft from where it was hit. The acceleration of gravity is 32 ft/s^2.

How high is the fence in feet?"

Now on to my questions:

1)No initial velocity is given, so can I assume that the initial velocity in the y-direction is 0?

NO, you can't assume that or the ball would never get off the ground! What you can do is assume some angle θ so that the velocity in the x-direction is v₀ cos(θ) and the velocity in the y-direction is v₀ sin(θ) where v₀ is the initial speed of the ball.
Now, set up the equations of motion for the x and y coordinates. They will involve two as yet unknown quantities: v₀ and θ. Use those to determine the maximum height of the ball and the time it reaches that maximum height- still depending on v₀ and θ. Set the time equal to 8.2 seconds. That gives you one equation in two unknowns.
You also are told that the ball has gone horizontally 800 ft when t= 8.2+ 0.6= 8.8 seconds. That gives you a second equation for the two unknowns v₀ and θ. You can solve for them!

2)How can I solve for the missing time that it takes the ball to clear the fence itself from t=8.8 seconds when it reaches the top of the fence?

What missing time? t= 8.8 seconds! Now that you have solved for v₀ and θ, set t= 8.8 in the y equation and find the height of the fence!

I'm not looking for answers or for anyone to work the problem for me, only answers to those questions.

Do you realize that sentense parses as "I'm not looking for answers, I'm only looking for answers"?