A rock is dropped from a bridge to the water below. It takes 2.40 s for the rock to hit
the water. Find the speed (in m/s) of the rock as it hits the water. How high (in
metres) is the bridge above the water?
a. V = Vo + g*t = 0 + 9.8*2.40 = 23.5 m/s.
b. h = 0.5g*t^2 = 4.9*2.40^2 = 28.2 m.
Well, let's start with the speed of the rock. Since the rock is dropped, we know that its initial velocity is 0 m/s. So, the final velocity can be found using the formula v = u + gt, where v is the final velocity, u is the initial velocity (which is 0), g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time taken (2.40 s).
Plugging in the values, we get v = 0 + (9.8 m/s^2)(2.40 s). Crunching the numbers, we find that the final velocity of the rock as it hits the water is 23.52 m/s. That's quite a splash!
Now, let's move on to the height of the bridge. We can use another formula: h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity, and t is the time taken (2.40 s). Plugging in the values, we get h = (1/2)(9.8 m/s^2)(2.40 s)^2.
Doing the math, we find that the height of the bridge above the water is approximately 28.18 meters. That's quite a drop! Let's hope no one was standing below when the rock hit the water. Safety first, after all!
To find the speed of the rock as it hits the water, we can use the formula for the velocity of an object in free fall:
v = g * t
where
v is the velocity (speed) of the rock,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time it takes for the rock to hit the water.
Substituting the known values:
v = 9.8 m/s^2 * 2.40 s
v = 23.52 m/s
So, the speed of the rock as it hits the water is 23.52 m/s.
To find the height of the bridge above the water, we can use the formula for the distance traveled in free fall:
h = (1/2) * g * t^2
where
h is the height of the bridge,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time it takes for the rock to hit the water.
Substituting the known values:
h = (1/2) * 9.8 m/s^2 * (2.40 s)^2
h = 28.224 m
So, the height of the bridge above the water is 28.224 meters.
To find the speed of the rock as it hits the water, we can use the equation:
v = gt
Where v is the velocity or speed, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time it takes for the rock to hit the water.
Given that the time is 2.40 s, we can substitute these values into the equation:
v = 9.8 m/s² × 2.40 s
v = 23.52 m/s
So, the speed of the rock as it hits the water is 23.52 m/s.
To find the height of the bridge above the water, we can use a different equation known as the kinematic equation:
h = (1/2) × g × t²
Where h is the height, g is the acceleration due to gravity, and t is the time it takes for the rock to hit the water.
Using the same values as before, we can calculate the height:
h = (1/2) × 9.8 m/s² × (2.40 s)²
h = (1/2) × 9.8 m/s² × 5.76 s²
h = 28.224 m
So, the height of the bridge above the water is 28.224 meters.