Erica kicks a soccer ball 12 m/s at horizontally from the edge of the roof of a building which is 30.0 m high.
a. When does it strike the ground?
b. With what velocity does the ball strike the ground?
a. Well, Erica must have some impressive kicking skills! To find out when the ball strikes the ground, we can use the equation of motion for vertical motion: h = ut + (1/2)gt^2. Here, h is the height (which is 30.0 m), u is the initial vertical velocity (which is 0 m/s because the ball is only kicked horizontally), g is the acceleration due to gravity (which is approximately 9.8 m/s^2), and t is the time it takes for the ball to hit the ground. Plugging in the values, we get: 30.0 = 0 + (1/2)(9.8)t^2. Solving for t, we find t ≈ 2.18 seconds.
b. Now, let's find out the velocity at which the ball strikes the ground. Since the ball is only kicked horizontally, its initial vertical velocity (v) is 0 m/s. The final vertical velocity (v') when the ball hits the ground can be found using the equation v' = u + gt. Here, u is still 0 m/s, and t is the same as the time it took for the ball to hit the ground (which is approximately 2.18 seconds). Plugging in the values, we get v' = 0 + (9.8)(2.18) = 21.36 m/s. Therefore, the ball strikes the ground with a vertical velocity of approximately 21.36 m/s. Hold on to your hats!
To find the time it takes for the ball to strike the ground, we can use the basic kinematic equation:
h = vi*t + (1/2)*g*t^2
Where:
h = height of the building (30 m)
vi = initial vertical velocity (0 m/s, since the ball is only kicked horizontally)
g = acceleration due to gravity (-9.8 m/s^2, assuming downward direction)
t = time taken for the ball to reach the ground
First, let's find the time it takes for the ball to reach the ground:
30 = 0*t + (1/2)*(-9.8)*t^2
30 = -4.9t^2
t^2 = 30/(-4.9)
t^2 = -6.12245
t = sqrt(-6.12245) (taking square root to find the positive value)
t = √6.12245
t = 2.47 seconds (approx)
a. The ball will strike the ground after approximately 2.47 seconds.
To find the velocity at which the ball strikes the ground, we can use the equation of motion:
v = vi + g*t
vi = initial horizontal velocity (12 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time taken for the ball to reach the ground (2.47 seconds)
Now let's calculate the velocity at which the ball strikes the ground:
v = 12 + (-9.8)*2.47
v = 12 - 24.206
v = -12.206 m/s
b. The ball strikes the ground with a velocity of approximately -12.206 m/s. Note that the negative sign indicates that the ball is moving in the downward direction.
To calculate when the soccer ball strikes the ground and with what velocity it strikes the ground, we can use kinematic equations.
First, let's determine the time it takes for the ball to reach the ground:
We know the initial vertical velocity (Vy0) is 0 m/s since the soccer ball is kicked horizontally.
Using the equation:
h = Vy0 * t + (1/2) * g * t^2,
where h is the vertical displacement (30.0 m) and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can solve for t:
30.0 m = 0 * t + (1/2) * 9.8 m/s^2 * t^2
Simplifying the equation:
4.9 m/s^2 * t^2 = 30.0 m
Dividing both sides by 4.9 m/s^2:
t^2 = 30.0 m / 4.9 m/s^2
t^2 ≈ 6.12 s^2
Taking the square root of both sides:
t ≈ √6.12 s
t ≈ 2.47 s
Therefore, it takes approximately 2.47 seconds for the soccer ball to reach the ground.
To calculate the velocity with which the ball strikes the ground, we need to find the horizontal velocity (Vx) since there is no acceleration in the horizontal direction:
We know the initial horizontal velocity (Vx0) is 12 m/s.
Using the equation:
Vx = Vx0,
the horizontal velocity remains constant.
Therefore, the soccer ball strikes the ground with a horizontal velocity of 12 m/s.
In summary:
a. The soccer ball strikes the ground approximately 2.47 seconds after being kicked.
b. The ball strikes the ground with a horizontal velocity of 12 m/s.
Horizontal component doesn't effect the rate at which it falls, and we will treat up as positive
x=x(orignial)+v(original)t+0.5at^2
-30=0.5(-9.8)t^2
t=2.47s
v(final)=v(original)+at
v(final)=at
v=(-9.8)(2.47)
v=-24.2m/s