A projectile is fired with an initial speed of 180 m/s and...

A projectile is fired with an initial speed of 180 m/s and angle of elevation 60°. (Recall g ? 9.8 m/s². Round your answers to the nearest whole number.) (a) Find the range of the projectile. m (b) Find the maximum height reached. m (c) Find the speed at impact. m/s

Transcript

0:00 Hi there.

00:01 So for this problem, we are told that a projectile is fire with an initial speed.

00:05 So the initial speed for this is 180 meters per second.

00:10 And then this at an angle of elevation, let's label that as theta, that is equal to 60 degrees.

00:17 So with that said, so we are going to assume that the initial height of this is it is thrown from the ground level, and that will be then equal to zero.

00:27 So for the first question for part a is about to find the range of the projectile.

00:32 Now, the horizontal range is just initial speed times the cosine of theta times the time that it takes to get to the ground.

00:39 Now, to determine the time that it takes to get to the ground, we use the vertical motion of this.

00:44 So that will be the initial speed times the sign of theta times the time minus 1 divided by 2 the acceleration due to gravity times the time square.

00:54 Now we set this equal to zero because we want the time that it takes to get to the ground.

00:59 So that will be the initial speed times the sign of theta.

01:03 We can cancel one time in here.

01:06 That will be then minus 1 divided by 2 the acceleration due to gravity times the time.

01:11 Now we just need to solve for the time.

01:14 So the time that we obtain from this is equal to 2 times initial speed, the sign of theta, divided by the acceleration due to gravity.

01:21 So now let's substitute the values in here.

01:23 So that will be 2 times 180 for the initial speed times the sign of the angle.

01:29 The sign of the angle is 60 degrees.

01:33 And then this divided by the acceleration due to gravity that is 9 .8 meters per second square.

01:39 Then using our calculator, we obtain a value off.

01:48 Then the time that we obtained for this is 31 .81, okay, seconds.

01:54 So that's the time that it takes to get to the graph.

01:56 So that is the time that we need to substitute in here.

02:00 So the horizontal range for this is equal to 180 times the cosine of 60 degrees.

02:10 And then this times the time that we just determined, that is 31 .81.

02:16 Then using our calculator, we obtain a value of.

02:24 Okay, then the value that we obtained for this is equal to 2 ,800...

Question

A projectile is fired with an initial speed of 180 m/s and angle of elevation 60°. (Recall g ? 9.8 m/s². Round your answers to the nearest whole number.) (a) Find the range of the projectile. m (b) Find the maximum height reached. m (c) Find the speed at impact. m/s

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