projectile is launched horizontally from edge of cliff 20 m high with an initial speed of 10 m/s. what is the horizontal distance the projectile travels before striking the level ground below the cliff?
what formula do i use?
First the vertical problem:
How long to fall 20m?
0 = 20 + 0 t -(1/2)9.8 t^2
4.9 t^2 = 20
t = 2.02 seconds in the air
Now the horizontal problem:
How far in 2.02 seconds at 10 m/s?
20.2 meters
The end.
thanks!
To find the horizontal distance the projectile travels before hitting the ground, you can use the formula:
distance = speed × time
In this case, since the projectile is launched horizontally, its initial vertical velocity is 0 m/s, meaning it won't change while it is in the air. So, we can ignore the vertical motion and focus on the horizontal motion.
To find the time it takes for the projectile to hit the ground, we can use the formula:
time = distance / speed
In this case, the distance is the height of the cliff, which is 20 m, and the speed is the initial speed of the projectile, which is 10 m/s. Therefore, the time it takes for the projectile to hit the ground is:
time = 20 m / 10 m/s = 2 seconds
Now that we have the time, we can use it to find the horizontal distance:
distance = speed × time
distance = 10 m/s × 2 seconds = 20 meters
So, the projectile will travel a horizontal distance of 20 meters before hitting the ground below the cliff.
To find the horizontal distance the projectile travels before striking the ground, you can use the formula for horizontal distance:
Horizontal distance = (initial horizontal velocity) x (time of flight)
In this case, the projectile is launched horizontally, so the initial horizontal velocity is the same as the launch velocity. The time of flight is the time it takes for the projectile to reach the ground.
To calculate the time of flight, you can use the vertical motion formula:
Height = (initial vertical velocity) x (time) + (1/2)(acceleration due to gravity)(time)^2
Since the projectile is launched horizontally, the initial vertical velocity is zero. The height is given as 20 meters, and the acceleration due to gravity can be taken as -9.8 m/s^2 (assuming downwards is the positive direction).
Plugging in these values and rearranging the equation, you get:
0 = (-4.9)(time)^2 + 20
With a little bit of algebra, you can solve for the time:
(-4.9)(time)^2 = -20
(time)^2 = 20 / 4.9
time ≈ √(20/4.9)
Once you have the time of flight, you can plug it back into the horizontal distance formula:
Horizontal distance = (launch velocity) x (time of flight)
Substituting the given values:
Horizontal distance = (10 m/s) x (√(20/4.9))
Calculating this expression will give you the horizontal distance the projectile travels before striking the ground below the cliff.