A stone is dropped from a height of 49m and simultaneously another stone is thrown upwards from the ground with a speed of 40m/s.when and where do the two stones meet?

falling stone: hf=49-4.9t^2

rising stone: hf=0+40t-4.9t^2
set the equations equal (hf=hf), and solve for time t, then put that t into either of the original equations and solve for hf.

To find out when and where the two stones meet, we need to calculate the time it takes for each stone to reach the same height.

Let's start with the stone that is dropped from a height of 49m. We can use the equation:

h = 1/2 * g * t^2

Where:
h = height (49m)
g = acceleration due to gravity (9.8 m/s^2)
t = time

Rearranging the equation, we get:

t^2 = (2h) / g
t^2 = (2 * 49) / 9.8
t^2 = 98 / 9.8
t^2 = 10
t = sqrt(10)
t ≈ 3.16 seconds

So the stone dropped from 49m will take approximately 3.16 seconds to reach the ground.

Now, let's calculate the time it takes for the stone thrown upwards to reach the same height. We can use the equation:

h = u * t + 1/2 * g * t^2

Where:
h = 49m
u = initial velocity (40m/s)
g = acceleration due to gravity (9.8 m/s^2)
t = time

Substituting the values, we get:

49 = 40t + 1/2 * 9.8 * t^2
49 = 40t + 4.9t^2
4.9t^2 + 40t - 49 = 0

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 4.9, b = 40, and c = -49.

t = (-40 ± sqrt(40^2 - 4 * 4.9 * -49)) / 2 * 4.9
t ≈ 1.936 seconds or t ≈ -5.075 seconds

Since time cannot be negative in this scenario, we can ignore the negative value.

Therefore, the stone thrown upwards will take approximately 1.936 seconds to reach the same height.

Now, let's find the meeting point by calculating the distance covered by each stone during this time.

For the stone dropped from 49m, we can use the equation:

distance = 1/2 * g * t^2

distance = 1/2 * 9.8 * (3.16)^2
distance ≈ 48.99m

For the stone thrown upwards with an initial velocity of 40m/s, we can use the equation:

distance = u * t + 1/2 * g * t^2

distance = 40 * 1.936 + 1/2 * 9.8 * (1.936)^2
distance ≈ 77.99m

Therefore, the two stones meet approximately 49m from the ground, and the meeting occurs after approximately 1.936 seconds.