On a 100 meter high cliff, a cannon fires a cannonball with an initial speed of 50 m/s at an angle of 53° to the horizontal. The ball passes through its maximum height at point A, point B which is at the same height as the cannon, and strikes the ground at point C.
(a) Determine the amount of time that the cannonball is a projectile. (Seconds)
(b) find the components of the ball's velocity at the given points a,b,c, the ball's speed at that point, and the amount of time that elapses before the ball reaches that point.
for the initial time is 0 seconds and the initial speed is 50 m/s, my teacher explained it but I'm still so confused on how to solve it
the height of the ball is
h(t) = 100 + 50 sin53° * t - 4.9t^2
h=0 when t = 10.158
Vy = 50 sin53° - 9.8t
Vx = 50 cos53°
So find t at the points A,B,C
B is the vertex, which is at t = -b/2a = 50 sin53°/9.8
the speed is, of course, √(Vx^2 + Vy^2)
yeah i understand that part, but how am i suppose to get the other points using that if i only know the first velocity which is 50 m/s
oobleck told you:
Vy = 50 sin53° - 9.8t
Vx = 50 cos53°
Vx NEVER CHANGES, (no force in horizontal direction)
You are at the vertex (top) when Vy = 0
the ball hits ground when h = 0, t = 10.158, you can find Vy then and of course you know Vx
To solve this problem, we can break it down into several steps.
Step 1: Analyze the motion
The cannonball follows a projectile motion, meaning it moves in a curved path under the influence of gravity. We need to find various properties of the projectile, such as the time it remains a projectile, velocity components at different points, speed at different points, and the time taken to reach those points.
Step 2: Break down the initial velocity
The initial velocity of the cannonball can be broken down into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component changes due to the effect of gravity.
Step 3: Find the time of flight
The time of flight is the total time for which the cannonball remains in the air. We can find it using the vertical component of the initial velocity and the acceleration due to gravity.
Step 4: Determine the velocity components at point A
At point A, the cannonball reaches its maximum height. We can find the vertical component of velocity using the time of flight. The horizontal component remains constant.
Step 5: Determine the velocity components at point B
At point B, the cannonball is at the same height as the cannon. The vertical component of the velocity remains the same as it was at point A. The horizontal component also remains constant.
Step 6: Determine the velocity components at point C
At point C, the cannonball strikes the ground. We can find the vertical component of velocity using the time of flight and the acceleration due to gravity. The horizontal component remains constant.
Step 7: Find the speed at each point
To find the speed at each point, we can use the Pythagorean theorem to calculate the magnitude of the velocity vector.
Step 8: Find the time taken to reach each point
Lastly, we need to determine the time taken to reach each point. This can be done using the horizontal velocity and dividing the horizontal distance by it.
By following these steps, we can solve the problem and find all the required quantities.