Answer :
- v = 4.02 m/s
- angle = 54.9° above the horizontal (which is 35.1° from the vertical)
- That is .552 m above the board, or 4.552 m above the water
- v = 9.72 m/s
- angle = 76.6° below the horizontal (which is 13.4° from the vertical)
Explanation:
write and understand the given problem
a)
Solve the x component
d = vt
3 = v(1.3)
v = 2.308 m/s in the x direction
Then for the y...
d = vot + 0.5 at^2
-4 = v (1.3) + (0.5) (-9.8) (1.3) ^2
v = 3.29 m/s
Now we can solve a)
The total initial velocity is from the Pythagorean theorem
v2 = (3.29) ^2 + (2.308) ^2
v = 4.02 m/s
b)
The direction from the tangent function
tan (angle) = 3.29 / 2.308
angle = 54.9° above the horizontal (which is 35.1° from the vertical)
c)
Apply vf ^2 = vo ^2 + 2ad in the y direction
0 = 3.292 + 2(9.8) (d)
d = 0.552 m
That is .552 m above the board, or 4.552 m above the water
d)
to find the y direction
vf^ 2 = vo^ 2 + 2ad
vf^ 2 = (3.29) ^2 + 2 (9.8) (4)
v = 9.45 m/s
Find the net by the Pythagorean Theorem
v^ 2 = (9.45) ^2 + (2.308) ^2
v = 9.72 m/s
e)
Direction by the tangent function
tan (angle) = 9.72 / 2.308
angle = 76.6° below the horizontal (which is 13.4° from the vertical)