a cannonball is fired straight up at 60m/s. how long does the flight last?
Twice the time that it takes to reach maximum height. That is when the velocity is zero. t = Vo/g at that time.
jenkins
To determine how long the flight of the cannonball lasts, we can use the equation of motion:
h = v₀t - 0.5gt²
where:
h = maximum height reached by the cannonball (which is 0 in this case because it is fired straight up and comes back down)
v₀ = initial velocity of the cannonball (which is 60 m/s)
t = time taken for the flight
g = acceleration due to gravity (which is approximately 9.8 m/s²)
Since the cannonball reaches its maximum height at the midpoint of its flight, we can find the time taken for the flight by doubling the time it takes to reach the maximum height.
First, let's find the time it takes to reach the maximum height:
0 = v₀t - 0.5gt²
Rearranging the equation, we have:
0.5gt² = v₀t
0.5g = vt/t
0.5gt = v₀
t = 2v₀/g (since the time to reach the maximum height is half the total flight time)
Now we can substitute the values into the equation:
t = 2 * 60 m/s / 9.8 m/s²
Calculating this, we have:
t ≈ 12.24 s
Therefore, the flight of the cannonball lasts approximately 12.24 seconds.
To find out how long the flight of the cannonball lasts, we need to use kinematic equations from physics. Specifically, we can use the equation for vertical motion under constant acceleration:
\[ \Delta y = v_{i}t + \frac{1}{2}a t^2 \]
Where:
- Δy is the change in vertical position (altitude)
- \( v_{i} \) is the initial velocity
- a is the acceleration
In this case, the cannonball is fired straight up, so the initial velocity is 60 m/s. The acceleration due to gravity is -9.8 m/s^2 (negative because gravity acts in the downward direction).
Since the cannonball reaches its maximum height at its peak, the change in vertical position, Δy, will be zero. We can set up the equation as follows:
\[ 0 = v_{i}t + \frac{1}{2}a t^2 \]
Plugging in the values:
\[ 0 = 60t - 4.9t^2 \]
To find the time, we can rearrange the equation and solve for t. In this case, we have a quadratic equation. By solving it using the quadratic formula or factoring, we can find the values of t.
After solving the equation, we find two possible values for time: t = 0 seconds and t = 12.24 seconds.
However, since the time t = 0 refers to the initial moment when the cannonball is fired, we discard that solution.
Therefore, the flight of the cannonball lasts approximately 12.24 seconds.