A golf ball is hit at ground level at an angle of 31.9° above the horizontal. Its range is 257 m over a level green. What was the magnitude of the golf ball's initial velocity?

Hey, guys. Let's check out this practice problem here. We've got a golf ball that's hit at some angle and we know the range and we're gonna figure out the magnitude of the ball's initial velocity. So I'm just gonna draw a quick little sketch here. We're told that this golf ball is hit over a level green, which is important because that means that we know that it's going to be a symmetrical launch. A level green means it's gonna come back down to the same height at which it was, through you know, launched at. Right? So we know we're dealing with a symmetrical launch problem, which is great. So we can use our symmetrical launch equations. So what are we told? We're told the launch angle is 31.9 degrees. And the other thing we know is we know that the range over the level green, which is r, is equal to 257 meters. So what are we trying to find? We're trying to find the initial velocity here. So if we go over to our special equations, we have 2. We have t symmetrical and range symmetrical or r symmetrical. And remember that both of these equations depend or have v naught, theta, and g. Right? So what you basically just need to do is figure out which equation we're going to use, and that comes down to which equation we know the most information about. So let's take a look for exam for example. What about the time symmetrical? So do we know anything, any information about the time that it takes for this ball to go up and then come back down again? We don't. So because we don't know time here, let's go to the range equation. Because we actually know the distance that this ball covers over the level green, we do know our symmetrical, so therefore we're gonna use that equation. So it really just comes down to that, right? So we have our symmetrical is equal to V naught squared times the sine of 2 theta divided by g. Now we have g is, we also know what the launch angle is, this is the 31.9 degrees, and we know what the range is. So the only thing we really need to figure out is just this v naught. We only have one unknown so we're just gonna go ahead and solve. Right? It's just as straightforward as that. So what we do here is we're gonna move g over to the other side. This is gonna be g times r symmetrical. Then we're gonna divide the sine to the other side, and that just leaves us with V naught squared over here. So what we're gonna do is we're just gonna take the square roots and I'm just gonna start plugging all the numbers in. So I have 9.8. I have the range as 257. Then I've got the sine of 2 times 31.9 degrees. You go ahead and just plug all that stuff into your calculator. You're gonna get the initial velocity, which is 53 meters per second. So that is the answer and that happens to be answer choice d. Alright guys. That's it for this one. Let's keep going.

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A golf ball is hit at ground level at an angle of 31.9° above the horizontal. Its range is 257 m over a level green. What was the magnitude of the golf ball's initial velocity?

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