Write an exponential function to model the following situation.
1 answer:
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Answer:
a) 63.6 ft
b) 1.99 seconds
c) 4.98 seconds
Step-by-step explanation:
a) The object will reach maximum height when its final velocity, v, is 0 m/s.
We apply one of Newton's equations of motion to solve this:
where u = initial velocity = 64 ft/s
g = acceleration due to gravity = 32.2 ft/s
h = height reached by object.
Note: the equation has a negative sign because the object is going upwards, against gravity.
Hence:
The object is now 63.6 ft above the platform (143.6 ft above the ground).
b) Time taken to get to that height can be gotten by using another one of Newton's equations:
=>
It took the object 1.99 secs to get to that height.
c) When the object begins falling to ground level, it is at a height, h = 143.6 ft and begins moving at initial velocity, u = 0 m/s.
Applying another of Newton's equations of motion, we have that:
where t is the time taken to hit the floor after it begins its descent.
Therefore,
This is the time it will take the object to hit the floor after it begins its descent.
Therefore, the total time it will take for the object to hit the ground after it is launched will be:
T = time taken to reach maximum height + time taken to hit the floor after it begins descending
T = 1.99 + 2.99
T = 4.98 seconds
The scale factor of the dilation from ABCD to A′B′C′D′ is 3.
Step-by-step explanation:
Step 1:
In the pre-image ABCD, the length of one of the sides is given as 14 units.
For the other shape A′B′C′D′, the same side as the previous shape is given as 8 units.
Step 2:
To determine the scale factor, we divide the measurement after scaling by the same measurement before scaling.
In this case, it is the given length of the sides CD and C′D′.
So the scale factor =
So the shape ABCD is dilated by a scale factor of to produce the shape A′B′C′D′.