SOLUTION: Please help me with the following word problems: 1) A rock falls from a tower that is 122.500002 m high. As it is falling, its height is given by the formula h=122.500002 - 4.9t2

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Question 86899: Please help me with the following word problems:
1) A rock falls from a tower that is 122.500002 m high. As it is falling, its height is given by the formula h=122.500002 - 4.9t2 with t in seconds. How many seconds will it take for the rock to hit the ground (h = 0)?
2) A ball is dropped from a cliff that is 352 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S=16t2 How many seconds (to tenths) will it take for the ball to hit the ground?
3) A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s=16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 81 feet?
4) The length of a rectangular frame is 5 cm more than the width. The area inside the frame is 66 square cm. Find the width of the frame.
Answer by Flake(45) About Me  (Show Source):
You can put this solution on YOUR website!
We can use Quadratic equaltion to solve these.
---We should try to write each of the problems into aX%5E2+%2B+bX+%2B+c+=+0
---Then solve with x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
****Sorry for being long winded, but thought I try to set a good foundation********
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1) A rock falls from a tower that is 122.500002 m high. As it is falling, its height is given by the formula h=122.500002 - 4.9t2 with t in seconds. How many seconds will it take for the rock to hit the ground (h = 0)?
---Step#1: Understand and visualize the problem.
Imaging you're on the tower and about to drop the rock.
At time-zero, did the rock travel any distance? NO. Because you have not let it go. It should be 122.500002 m from the ground.
At t=0 we should have h=122.500002
h=122.500002+-+4.9t%5E2+
h=122.500002+-+4.9%280%29%5E2+
h=122.500002+-+0+=+122.500002+
Now you drop the rock. The rock start travelling down towards the ground. Until at time-final, the rock hits the ground and stops.
How far did the rock? It travel the entire height of the tower, which is 122.500002 m. How high is it from the ground? Zero height from the ground because the rock is on the ground, so h = 0
---Step2: How many seconds will it take for the rock to hit the ground?
At t=t-final, the height should be Zero
h=122.500002+-+4.9t%5E2
0=122.500002+-+4.9t%5E2
4.9t%5E2+=+122.500002+
t%5E2+=+122.500002%2F4.9+
t+=+sqrt%28122.500002%2F4.9%29+=+aprx.+5+sec.
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#2 can be solve the same ways as #1
#3 is similar by rewriting the problems into aX%5E2+%2B+bX+%2B+c+=+0. Then solve with x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
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#4 The length of a rectangular frame is 5 cm more than the width. The area inside the frame is 66 square cm. Find the width of the frame.
A = LW; where L=(5+W) and A = 66
66+=+%285+%2B+W%29W+
66+=+5W+%2B+W%5E2+
W%5E2+%2B+5W+-+66+=+0+
Now solve with x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+