Respuesta :
Answer:
1. h = h₀ + u×t - 1/2×g×t²
2. 2.95 s
3. 152.14 ft
4. 3.07 s
Step-by-step explanation:
The given parameters are;
Vertical velocity of the balloon = 95 ft/s
Height from which the balloon is released = 12 feet
The function is h = h₀ + u×t - 1/2×g×t²
Where:
h = Height of the balloon at time t
h₀ = Initial height of the balloon = 12 feet
u = Initial upward velocity of the balloon = 95 ft/s
t = Time duration of motion
g = Acceleration due to gravity = 32.2 ft/s²
2. The time to maximum height is found from;
v = u - g·t
Where:
v = Final velocity = 0 m/s at maximum height
∴ 0 = 95 - 32.2 × t
32.2·t = 95
t = 95/32.2 = 2.95 s
Therefore, the time it will take to reach maximum height = 2.95 s
3. From h = h₀ + u×t - 1/2×g×t², we have;
h = 12 + 95×2.95 - 1/2×32.2×2.95² = 152.14 ft
4. Therefore;
152.14 = 0×t + 1/2 × 32.2 × t²
t² = 152.14/16.1 = 9.45 s
t = √9.45 = 3.07 s
Answer:
The function is: y(t) = 12 + 95*t - 16.085*t²
The time it'll take to reach the maximum height is: 2.95 s
The maximum height is: 152.27 ft
The time it'll take to hit the ground is: 12 s
Step-by-step explanation:
The water ballon is under the constant acceleration of gravity, therefore it's movement can be modelled by the equations that describe constant acceleration movement, as shown below:
y(t) = y(0) + v(0)*t - 0.5*g*t²
The acceleration is negative, because they are contrary to the movement. Applying the data form the problem, we have:
y(t) = 12 + 95*t - 0.5*32.17*t²
y(t) = 12 + 95*t - 16.085*t²
This equation describes a parabolla, therefore the time at which it achieves the maximum height is the "x" coordinate for the vertex, which can be found by using the formula below:
t = (-b)/[2*a]
t = (-95)/[2*(-16.085)] = -95/(-32.17) = 2.95 s
And the maximum height is:
y(2.95) = 12 + 95*2.95 - 16.085*(2.95)² = 152.27 ft
The time it'll take to reach the ground is:
y(0) = 12 + 95*0 - 16.085*(0)² = 12 s
