00:02
Hi, in this question it is given that a car travels along a straight road with a constant speed of v is equal to 60 miles per hour.
00:11
So the velocity is given us 60 miles per hour.
00:21
Let us convert it into feet per second.
00:26
For that, 60 divided by 0 .68182.
00:40
60 divided by 0 .68182, we obtain 88 feet per second.
00:50
This is the velocity with which the car is moving along a straight road.
00:55
At the instant, when the angle theta is equal to 60 degrees, we need to determine the rate at which the angle theta varies with respect to time in radiance per second.
01:07
And d is given.
01:09
Let us assume this is the car.
01:10
This is moving with the velocity of 60 miles per hour, that is 88 feet per second.
01:17
And let us consider this is the x direction and this is the y direction, x axis and y axis.
01:22
And this is making an inclination of 64 degrees.
01:25
We need to find the angular velocity or we can say that the angle theta changes with respect to time.
01:37
Now let us find the distance or this r.
01:40
We know this d is equal to 88 feet.
01:47
From the configuration we can find that r is equal to y by sine theta, where this y is this 88 feet and theta is 64 degrees.
02:06
So 88 divided by sine 64, we obtain r is equal to.
02:18
98 feet...