baloonist drops rock from balloon. takes 7 seconds for the rock to fall. what's the balloonist's altitude in feet?
1101 feet
To find the balloonist's altitude, we can use the formula for the distance an object falls under the force of gravity:
d = (1/2) * g * t^2
Where:
- d is the distance
- g is the acceleration due to gravity (32.2 ft/s^2)
- t is the time (7 seconds)
Plugging in the values, we get:
d = (1/2) * 32.2 ft/s^2 * (7 s)^2
Simplifying further:
d = 0.5 * 32.2 ft/s^2 * 49 s^2
d = 803.8 ft
Therefore, the balloonist's altitude is approximately 803.8 feet.
To calculate the balloonist's altitude in feet, we can use the equation for the distance traveled by a falling object:
d = 0.5 * g * t^2
where:
d = distance
g = acceleration due to gravity (32.2 ft/s^2)
t = time
In this case, the time is given as 7 seconds, so we can plug in that value and solve for the distance:
d = 0.5 * 32.2 ft/s^2 * (7 s)^2
d = 0.5 * 32.2 ft/s^2 * 49 s^2
d = 0.5 * 1577.8 ft
d ≈ 788.9 ft
Therefore, the balloonist's altitude is approximately 788.9 feet.
It will depend upon whether the balloon is rising or falling when the rock is released.
If the balloon altitude is constant at release of the rock,
Y = (g/2)*t^2
is the distance it falls in time t
g = 32.2 ft/s^2 t = 7 s
Solve for the altitude Y