A baseball is seen to pass upward by a window with a vertical ...

Question

A baseball is seen to pass upward by a window with a vertical speed of 13 m/s. If the ball was thrown by a person 18 m below on the street, when was it thrown?

Accepted Answer

Hey, everyone in this problem, a toy rocket is spotted ascending vertically past the edge of a cliff with a vertical speed of 10 m per second. The rocket was launched from the base of the cliff which is 30 m below the cliff's edge. Whereas to determine the time between when it was launched to when it was seen passing the edge of the cliff, we're given four answer choices all in seconds. Option A 1.02 option B 0.6 option C 1.47 and option D 1.66. Ok? So first thing we're gonna do is draw a little diagram. So we have our cliff and it has a height of 30 m. We're gonna have our toy rocket launched from the base of that cliff with some initial speed and it's gonna be seen passing the cliff's edge with the speed which we're gonna call our final speed. VF of 10 m per second. Ok. We wanna know how long this takes. So let's go ahead and write out all the information we were given and see what we can do. Ok? So we aren't told that initial speed be not that launch speed. Ok. We do know that the final speed or the speed as the rocket passes, the cliff's edge is going to be 10 m per second. And we're gonna take that to be positive. So we're saying that upwards is our positive direction delta y the change in position or the displacement of the rocket in the vertical direction is 30 m. Say that height of that cliff, we wanna know how long this takes. That's our time tea. And we know that we have the acceleration due to gravity, which is gonna be negative 9.8 m per second squared. OK. We have a negative because that acts in the downwards direction and we've chosen up to be our positive direction. All right. So we have three known values which is enough with our kinematic equations to solve for the next. OK. However, what you'll notice is that all the kinematic equations require knowing von, right. So before we can find t we actually need to know VNO first, there is no kinematic equation with VF delta YT and a those known values in the time that we're looking for. OK. So we're gonna start with step one by finding VNO and then we'll go ahead and find tea once we know that. All right. So to find V knot, we're gonna choose the equation with V knot, the one we're looking for and the other three variables that are not VF delta Y and A and that equation is gonna be VF squared is equal to V knot squared plus two multiplied by a multiplied by delta Y substituting in our values 10 m per second, all squared is equal to V not squared plus two, multiplied by negative 9.8 m per second squared, multiplied by 30 m. We're gonna go ahead and simplify. On the left hand side, we have 100 m squared per second squared. That's gonna be equal to V knot squared minus 588 m squared per second squared. We can move this 588 to the left hand side by adding it to both sides. When we get that V knot squared is equal to 688 m squared per second squared, which means that V not is going to be the square root of 688 m squared per second squared. Now we're gonna leave it like that so that we can avoid as much round off error as possible. And once we get to our final calculation and the next step, we will approximate that square root. OK? But for now we'll just leave it like that now that we have V not, we can get to finding the time T, which is what we actually wanna find. OK? And now we know all the other variables. So we're just gonna choose any equation, any kinematic or U AM equation. That includes the time T, since that's what we're looking for. And the simplest one to use is gonna be VF is equal to VN plus a multiplied by T substituting in our values here, 10 m per second is equal to the square root of 688 meters per second plus negative 9.8 m per second squared multiplied by the time T OK. We rearrange for install for tea. We have that T is gonna be 10 m per second minus the square root of 688 meters per second. All divided by negative 9.8 meters per second squared. Ok. So we subtract the square root first and then we're gonna divide everything by that acceleration in order to isolate for the time T and we get that the time tea is equal to about 1.6561 seconds. And that is the time it takes for this toy rocket from launch to when it's seen passing the edge of the cliff, going back to our answer choices. We're going round to three significant digits. We can see that the correct answer is going to be option D 1.66 seconds. Thanks everyone for watching. I hope this video helped see you in the next one.

A baseball is seen to pass upward by a window with a vertical speed of 13 m/s. If the ball was thrown by a person 18 m below on the street, when was it thrown?

Key Concepts

Kinematics

Projectile Motion

Acceleration due to Gravity

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