Rates of Change Question. How to do this?
The equation of the path of a bullet fired into the air is y = −20x(x − 20), where x and y are displacements in metres horizontally and vertically from the origin. The bullet is moving horizontally at a constant rate of 1 m/s.
(a) Find the rate at which the bullet is rising:
(i) when x=8, , (ii) when y=1500.
(b) Find the height when the bullet is:
(i) rising at 30 m/s, (ii) falling at 70 m/s.
(c) Use the gradient function dy/dx to find the angle of flight when the bullet is rising at 10 m/s.
(d) How high does the bullet go, and how far away does it land?
The equation of the path of a bullet fired into the air is y = −20x(x − 20), where x and y are displacements in metres horizontally and vertically from the origin. The bullet is moving horizontally at a constant rate of 1 m/s.
(a) Find the rate at which the bullet is rising:
(i) when x=8, , (ii) when y=1500.
(b) Find the height when the bullet is:
(i) rising at 30 m/s, (ii) falling at 70 m/s.
(c) Use the gradient function dy/dx to find the angle of flight when the bullet is rising at 10 m/s.
(d) How high does the bullet go, and how far away does it land?
1 Answer
Kindly go through the Explanation Section.
Explanation:
Given that,
Here,
displacements from the origin of the bullet.
So,
moving horizontally & rising.
As,
Part (a)(i)
(a)(ii):
Part (b)(i):
The bullet is rising at
At this
(b)(ii):
The height
similarly be worked out by taking
Part (c):
We require
Now,
So,
But, we know that
So, if the angle of flight is
Part (d):
For the maximum height