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A boy throws a baseball onto a roof and it rolls back down and off the roof with a speed of 3.75 $\mathrm{m} / \mathrm{s}$ . If the roof is pitched at $35.0^{\circ}$ below the horizon and the roof edge is 2.50 $\mathrm{m}$ above the ground, find (a) the time the baseball spends in the air, and (b) the horizontal distance from the roof edge to the point where the baseball lands on the ground.

a. (a) $t = 0.53 \mathrm { s }$

b. (b) $s = 1.63 \mathrm { m }$

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party we first need to find, of course, the baseballs time of flight. And so we can then say that first V Y final squared equals the Y initial squared plus two times the acceleration or two times the acceleration, the direction times delta Why? And so we can say that then V y final is gonna be equal in the square root of V Y initial, which we know to be 3.75 meters per second multiplied by sine of this would be negative 35 degrees quantity squared minus two times G negative, 9.80 meters per second squared multiplied by negative 2.50 meters extend the square root and we find that the why final is equaling negative 7.32 meters per second were saying negative. We haven't amount. We have ah, negative in front. Um because we know that this is essentially actually being traveling downwards, So this would be downwards. And so we can then say that v y final equals the why initial plus g t to find time. And so time is gonna be equaling negative 7.32 meters per second minus and then we could say minus 3.75 meters per second, multiplied by sine of negative 35 degrees, all divided by negative 9.80 meters per second squared. And we find that then T is equaling 0.5 to 8 seconds. This is our baseball. The baseballs. Time of flight for part A. Now, for part B. We know that the, um there isn't any acceleration in the ex direction. So we can say our horizontal range would be equaling the velocity and next direction multiplied by t. This would be equaling 3.75 meters per second, multiplied by co sign of again negative 35 degrees multiplied by 0.5 to 8 seconds. And this is giving us 1.62 meters. This would be the horizontal range of the baseball. That is the end of the solution. Thank you. Feel watching