00:02
A tennis player wins a match at the stadium and hits a ball into the stance at 19 .4 meters per second and then an angle of 65 .5 degrees above the horizontal.
00:14
So that's labeled that as our initial velocity equal to 19 .4 meters per second and the initial angle of 65 .5 degrees.
00:27
Now, the spectator who catches the ball is at a height of 10 meters.
00:39
So we'll place that as h equals 10 meters.
00:44
And we are asked to find the time the ball reaches the spectator.
00:49
So to get the time, we use the equation for the projectile, and that is y is equal to v initial y times time minus one half gt squared where v iy is the initial velocity in the y component so the height in we are looking for is 10 meters so that's based it here as y and then the initial velocity in the y component can be acquired by multiplying the initial velocity with the sine theta function.
01:33
So that is 19 .4 meters per second times sine theta.
01:39
But we have a value for theta and that is 65 .5 degrees.
01:47
And then the unknown variable time and then the second term, we have one half times 9 .8 meters per second squared times the square.
01:58
Now we could arrange the equation such that the left side.
02:04
Side is equal to 0, and then simplifying all the factors per term will have 0 equals 10 or negative 10 .0 meters plus 17 .65 t minus 4 .9t squared.
02:27
So this factor here is equal to 17 .65 and this factor here is equal to 4 .9.
02:37
Then let's multiply the whole equation by negative.
02:41
We'll have 4 .9 t squared minus 17 .65 t plus 10 equals 0.
02:51
So we now have a second order equation where we can use the quadratic formula to derive the value of time.
03:01
So that is t equals negative b plus and minus squared of b squared minus 4ac.
03:11
D divided it by 2a.
03:15
So this one is our a value, this one is our b value, and this one is our c value.
03:25
Now substitute that into the quadratic equation, our quadratic formula, will have negative times, negative 17 .65 plus and minus squared of negative 17 .65 squared minus 4 times a times c.
03:50
Okay.
03:51
Then we divide it by two times four point.
03:55
So we have two ways into solving for t and one is by using this positive sign.
04:03
And then the other is for using the negative sign.
04:07
So if we use the positive sign, we'll get a value of 0.
04:15
We got the value of 2 .90 seconds.
04:21
And if we get a negative sign, we'll get a value of 0 .704 seconds...