A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 19.0 m/s. The cliff is h = 50.0 m above a flat horizontal beach.
With what speed and angle of impact does the stone land?
find the vertical speed at impact:
vf^2=2*g*h
You know the vertical velocity, and the horizontal velocity.
From that, you get the angle, and the magnitude.
I was able to find out the angle which is 57.83degree that is correct.
For the speed, i used sqrt(2*9.81*50)=31.32, is this correct because the hw site doesn't accept it. What am I missing?
Thanks.
The sqrt(2*9.81*50)= 31.32 (m/s) that you calculated is the vertical velocity compnent. There is also a horizontal component (19.0 m/s)
You need to combine them with the Pythagorean equatiuon to get the speed.
To determine the speed and angle of impact at which the stone lands, you can use the principles of projectile motion. Here's how you can calculate it step-by-step:
Step 1: Calculate the time it takes for the stone to hit the ground.
You can use the vertical motion equation:
h = (1/2)gt^2
where h is the height of the cliff (50.0 m) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Rearranging the equation to solve for time (t):
t = sqrt(2h / g)
Substituting the values, you get:
t = sqrt(2 * 50.0 / 9.8) = 3.19 seconds (rounded to 2 decimal places).
Step 2: Calculate the horizontal distance traveled by the stone.
Since the stone is thrown horizontally, there is no initial vertical velocity. The horizontal distance is given by the equation:
d = v_hor * t
where d is the horizontal distance, v_hor is the horizontal component of velocity, and t is the time calculated above. Since the stone is thrown horizontally, v_hor is equal to the initial horizontal velocity of the stone.
Step 3: Calculate the horizontal velocity of the stone.
The initial horizontal velocity is given as 19.0 m/s. Therefore, the horizontal velocity remains constant throughout the motion. So, v_hor = 19.0 m/s.
Step 4: Calculate the vertical velocity at impact.
The vertical velocity at impact can be determined using the equation:
v_vert = g * t
Substituting the values, you get:
v_vert = 9.8 * 3.19 = 31.262 m/s (rounded to 3 decimal places).
Step 5: Calculate the speed and angle of impact.
The speed at impact is the magnitude of the resultant velocity, which can be calculated using the Pythagorean theorem:
v_impact = sqrt(v_hor^2 + v_vert^2)
Substituting the values, you get:
v_impact = sqrt((19.0)^2 + (31.262)^2) = 36.581 m/s (rounded to 3 decimal places).
The angle of impact can be calculated using the inverse tangent function:
angle_impact = arctan(v_vert / v_hor)
Substituting the values, you get:
angle_impact = arctan(31.262 / 19.0) = 59.062 degrees (rounded to 3 decimal places).
Therefore, the stone lands with a speed of approximately 36.581 m/s and at an angle of approximately 59.062 degrees.