SOLUTION: A steel ball is projected downward at an angle of 48° with the horizontal from the top of the cliff 480 m high. Its initial velocity is 43 m/s. a. How long will it take before

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Question 1201880: A steel ball is projected downward at an angle of 48° with the horizontal from the top of the cliff 480 m high. Its initial velocity is 43 m/s.

a. How long will it take before striking the ground?
b. How far from the base of the building will it strike?
c. With what velocity will it hit the ground?
d. At what angle with horizontal will it strike?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A steel ball is projected downward at an angle of 48° with the horizontal from the top of the cliff 480 m high. Its initial velocity is 43 m/s.
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Using 10 m/sec/sec for gravity:

a. How long will it take before striking the ground?
The vertical component is -43*sin(48) = ~31.96 m/s
h(t) = -5t^2 - 31.96t + 480 = 0 at impact
Solve for t
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -5x%5E2%2B-31.96x%2B480+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-31.96%29%5E2-4%2A-5%2A480=10621.4416.

Discriminant d=10621.4416 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--31.96%2B-sqrt%28+10621.4416+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-31.96%29%2Bsqrt%28+10621.4416+%29%29%2F2%5C-5+=+-13.5020378419643
x%5B2%5D+=+%28-%28-31.96%29-sqrt%28+10621.4416+%29%29%2F2%5C-5+=+7.11003784196429

Quadratic expression -5x%5E2%2B-31.96x%2B480 can be factored:
-5x%5E2%2B-31.96x%2B480+=+%28x--13.5020378419643%29%2A%28x-7.11003784196429%29
Again, the answer is: -13.5020378419643, 7.11003784196429. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B-31.96%2Ax%2B480+%29

Ignore the negative value.
t = 7.11 seconds to impact
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b. How far from the base of the building will it strike?
Horizontal component = 43*cos(48)
Distance = 7.11*43*cos(48) = ~ 204.57 meters
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c. With what velocity will it hit the ground?
Impact speed = vert comp of 43 + 5t = 31.96 + 7.11*5 = ~ 67.51 m/sec
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d. At what angle with horizontal will it strike?
The path of the object is a parabola --- h(t) = -5t^2 - 31.96t + 480 = 0 at impact.
Find the slope at t = 7.11
h'(t) = -10t - 31.96 = -103.06
Angle = 180 - h'(t) = 76.94 degs

Answer by ikleyn(52813) About Me  (Show Source):
You can put this solution on YOUR website!
.
A steel ball is projected downward at an angle of 48° with the horizontal from the top of the cliff 480 m high. Its initial velocity is 43 m/s.
a. How long will it take before striking the ground?
b. How far from the base of the building will it strike?
c. With what velocity will it hit the ground?
d. At what angle with horizontal will it strike?
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Don't you think that 480 m is too much for the cliff ?

Also, can you explain that mysterious way how the cliff
transformed and became a building in the course of this problem ?


Or, may be, you mistakenly think that these two notions/conceptions are the same ?


The problems, written so inaccurately and carelessly, arouse compassion.


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The genesis of this problem in time is more than obvious.

Initially, it was normal problem with the cliff of 48 m high and a stone.

Then somebody decided to create his (or her) own problem.
This person changed 48 m to 480 m (without hesitation);
then replaced the cliff to a building (but not everywhere, since he/(she) forgot to check all appearances),
and finally replaced a stone by a steel ball - - -
- - - voila (!) - and new problem is just ready.

Or, may be, three (or even more persons) transformed the initial problem,
by replacing different words three times successively and getting three new problems.


If they continue to invent new problems using the same approach,
then the next problem will come with 4800 meters cliff and a ball made of platinum.