A child standing on the edge of a sheer cliff wall throws a rock down towards the ground below. The rock is thrown 67° below the horizontal at a speed of 22 m/s & lands 43 m from the base of the cliff wall. Ignore air drag.
A.) Determine how long the rock was in the air.
s
B.) Determine how high the cliff wall is.
m
C.) Determine how fast the rock was going upon impact.
m/s
D.) Determine the angle of impact.
°
a) Use delta x= V * delta t
43 m= 22 m/s*cos 67 *delta t
delta t= 5.00 s
b) Use delta x= Vo*delta t + 1/2 * a* delta t ^2
delta x= 22 m/s*sin(-67)(5.00s)+ 1/2 *-9.81 m/s^2 * (5.00s)^s
delta x= -223.88m
Since the rock went down 223.88m, the cliff is 223.88 m high.
c)Use Vf^2-Vo^2= 2a*deltax
Vf= sqrt (2a*deltax+Vo^2)
Vf= +- sqrt |(2*-9.81m/s^2*-223.88m+(22m*sin(-67))^2)|
Vf=-69.301 m/s
However, this is only the y component. Use Pythagorean theorem to find the final velocity:
Final velocity = sqrt (-69.301m/s ^2 + 22*cos(-67) ^2)
Final velocity=69.832 m/s
d) use arctan to find the angle of impact. arctan (-69.301/(22*cos(-67))
Angle= -82.929
Hope this helps!
To solve this problem, we can break it down into four parts:
A.) Determining how long the rock was in the air.
B.) Determining how high the cliff wall is.
C.) Determining how fast the rock was going upon impact.
D.) Determining the angle of impact.
Let's go through each of these steps:
A.) To determine how long the rock was in the air, we can use the horizontal motion of the rock, as there is no horizontal acceleration due to air drag. We can use the equation:
distance = initial velocity * time + 0.5 * acceleration * time^2
In this case, the initial velocity is the horizontal component of the rock's velocity, which can be found using the given speed and angle. The acceleration is 0 since there is no horizontal acceleration. The distance is the horizontal distance the rock travels, which is given as 43 m.
Using the given speed of 22 m/s and angle of 67° below the horizontal, we can find the horizontal component of the velocity using the equation:
horizontal velocity = speed * cos(angle)
Substituting the known values, we get:
horizontal velocity = 22 m/s * cos(67°)
Now we can rearrange the distance equation to solve for time:
time = (distance - 0.5 * acceleration * time^2) / initial velocity
Plugging in the values, we have:
43 m = (horizontal velocity * time)
time = 43 m / horizontal velocity
Substituting the value of the horizontal velocity we found earlier, we can solve for time.
B.) To determine how high the cliff wall is, we need to use the vertical motion of the rock. The vertical distance traveled by the rock can be calculated using the equation:
vertical distance = initial vertical velocity * time + 0.5 * gravity * time^2
In this case, the initial vertical velocity is the vertical component of the rock's velocity, which can be found using the given speed and angle. The gravity acceleration is 9.8 m/s^2. The vertical distance is what we need to find.
Using the given speed of 22 m/s and angle of 67° below the horizontal, we can find the vertical component of the velocity using the equation:
vertical velocity = speed * sin(angle)
Substituting the known values, we get:
vertical velocity = 22 m/s * sin(67°)
Now we can rearrange the distance equation to solve for the vertical distance:
vertical distance = (vertical velocity * time) + (0.5 * gravity * time^2)
We can substitute the value of time we found earlier and solve for the vertical distance.
C.) To determine how fast the rock was going upon impact, we can use the vertical motion again. The rock's velocity upon impact can be calculated using the equation:
final velocity = initial vertical velocity + (gravity * time)
We already know the initial vertical velocity and the value of time. We can substitute these values and solve for the final velocity.
D.) To determine the angle of impact, we can use trigonometry. The tangent of the angle of impact can be calculated using the equation:
tangent(impact angle) = vertical velocity / horizontal velocity
We already have the values for both the vertical and horizontal velocities. We can substitute them and solve for the impact angle.
Once we have completed these steps, we will have the answers to all parts of the problem.