A projectile of mass 0.777 kg is shot from a cannon, at height 6.6 m, as shown in the figure, with an initial velocity vi having a horizontal component of 7.8m/s.
The projectile rises to a maximum height of ∆y above the end of the cannon’s barrel and strikes the ground a horizontal distance ∆x past the end of the cannon’s barrel.
----Find the vertical component of the initial
velocity at the end of the cannon’s barrel,
where the projectile begins its trajectory. The
acceleration of gravity is 9.8 m/s
2
no figure, no angle. can't figure vertical velocity
To find the vertical component of the initial velocity at the end of the cannon's barrel, we need to first understand the motion of the projectile.
Let's break down the problem step by step:
1. Find the time it takes for the projectile to reach its maximum height (∆y above the end of the cannon's barrel):
- We can use the vertical component of the initial velocity (viy) and the acceleration due to gravity (g) to find the time it takes to reach the maximum height using the equation: ∆y = viy * t + (1/2) * g * t^2, where ∆y is the maximum height.
2. Find the vertical component of the velocity at the maximum height (vfy):
- At the maximum height, the vertical component of the velocity becomes zero. Hence, vfy = 0.
3. Find the time it takes for the projectile to reach the ground (horizontal distance ∆x past the end of the cannon's barrel):
- We can use the horizontal component of the initial velocity (vix) and the horizontal distance (∆x) to find the time it takes using the equation: ∆x = vix * t.
4. Find the total time of flight:
- The total time of flight (T) is the sum of the time it takes to reach the maximum height and the time it takes to reach the ground. T = t + t.
5. Find the vertical component of the initial velocity at the end of the cannon's barrel (viy):
- Finally, we can use the equation: viy = vfy - g * T.
By plugging in the given values and solving these equations step by step, we can find the vertical component of the initial velocity at the end of the cannon's barrel.