00:01
In this problem on the topic of projectile motion, we are told that in an airplane that is flying horizontally with a given speed, an engine falls off.
00:10
If we ignore air resistance and we are given the time that it takes for the engine to hit the ground, we want to firstly show that the airplane is 4 .5 kilometers high.
00:20
Next, we want to show that the horizontal distance that the aircraft will cover in this time is 8 ,400 meters.
00:27
And finally we want to know where the engine would be relative to the airplane the moment the engine hits the ground.
00:38
So firstly, the vertical distance over which the engine falls is y.
00:48
And we know y is equal to v0t plus a half gt squared where v0 is the initial velocity.
00:55
But the vertical motion is zero.
00:58
So the initial velocity of the engine as it falls is zero.
01:03
And so it starts from rest and will fall a distance y of a high of half gt squared, where g is acceleration due to gravity.
01:14
So this is a half times we use the value 10 meters per square second as an estimate for gravity times the time over which it falls 30 seconds all squared.
01:29
So if you calculate this, we get this to be 4 ,500 meters...