00:01
Hi there, so for this problem, the expression that we are given is that the range of a projectile is equal to the initial speed squared.
00:12
This divided by 32, this times the sign of two times the angle theta.
00:22
So we need to use differentials to approximate the change in the range when the initial speed is given, and that is 27.
00:36
And the angle theta is changed from a value of 10 to 12 degrees.
00:51
What we need to do is to obtain the differential in the radius, which is the partial derivative of the radius with respect to the angle theta, this times the differential in the angle theta.
01:07
Now the differential in the angle theta is the difference between the two values given, 12 degrees minus 10 degrees.
01:16
So that will give us two degrees.
01:19
And the angle theta that we're going to use for this is the later value, which is 12 degrees.
01:26
Ok, so with that said, we just need to take the derivative of this expression with respect to the angle theta.
01:36
Let me just do that separately...