Answer:
Explanation:
To determine the time it will take for the object to hit the ground below, we can use the formula:
h = (1/2)gt^2 + vt + s
where:
h is the height, which is 25 meters
g is the acceleration due to gravity, which is -9.8 m/s^2 (negative because it acts downward)
v is the initial velocity, which is 135 m/s
s is the initial displacement, which is 0
t is the time we are trying to find
Substituting the values and solving for t, we get:
25 = (1/2)(-9.8)t^2 + 135t + 0
t^2 - (135/9.8)t - 2.551 = 0
Using the quadratic formula, we get:
t = 13.97 seconds
Therefore, it will take approximately 13.97 seconds for the object to hit the ground.
To determine the maximum height that the object will reach, we can use the same formula and find the height when the velocity is 0 (i.e., at the highest point):
h = (1/2)gt^2 + vt + s
v = u + gt
0 = 135 - 9.8t
t = 13.78 seconds
Substituting the values, we get:
h = (1/2)(-9.8)(13.78)^2 + 135(13.78) + 25
h ≈ 937 meters
Therefore, the maximum height that the object will reach is approximately 937 meters.
To find the length of the hypotenuse, we can use the Pythagorean theorem:
a = 2x + 2
b = x
c = 4x - 7
a + b + c = 30
2x + 2 + x + 4x - 7 = 30
7x - 5 = 30
7x = 35
x = 5
So the shorter leg is 5, the longer leg is 2(5) + 2 = 12, and the hypotenuse is 4(5) - 7 = 13.
Therefore, the length of the hypotenuse is 13.