Heather and Jerry are standing on a bridge 43m above a river. Heather throws a rock straight down with a speed of 12m/s . Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance.
Well, it sounds like Heather and Jerry are having a rockin' time on that bridge! But let's get down to business. Since both rocks are thrown with the same speed, we can say that they both have the initial velocity of 12 m/s.
Now, Heather's rock is thrown straight down, so it's headed towards the river. On the other hand, Jerry's rock is thrown straight up, defying gravity like a true rebel.
Since we're ignoring air resistance, both rocks will experience an acceleration of -9.8 m/s² due to gravity. Heather's rock will accelerate downwards, while Jerry's rock will decelerate until it reaches its maximum height and then comes back down.
The time it takes for Heather's rock to hit the river can be calculated using the formula: distance = velocity * time + 0.5 * acceleration * time². Since Heather is 43 m above the river, the distance is -43 m (negative because it's going down), the initial velocity is 12 m/s, and the acceleration is -9.8 m/s².
Solving for time, we eventually find that it takes Heather's rock approximately 1.4 seconds to reach the river. But hey, be careful, Heather!
As for Jerry's rock, it will take the same time to reach its maximum height as it will take to come back down. So, Jerry's rock will reach its highest point after approximately 0.7 seconds. After that, it will descend back to Earth gracefully, or maybe not so gracefully if Jerry's aim is off.
Remember, folks, always have fun but be mindful of the laws of physics. Safety first, especially when rock throwing is involved!
To find out when and where the rocks will meet, we need to determine their motion equations and solve them simultaneously.
Let's analyze the motion of Heather's rock first. Since she throws it straight down, we can take the acceleration due to gravity (g) as a positive value.
For Heather's rock:
Initial velocity (u1) = 12 m/s (downward)
Final velocity (v1) = ? (at the meeting point)
Time (t) = ? (at the meeting point)
Acceleration (a1) = +9.8 m/s^2 (downward, taking the gravitational acceleration as positive)
Using the kinematic equation:
v1 = u1 + a1 * t
Now let's analyze the motion of Jerry's rock. Since he throws it straight up, we take the acceleration due to gravity as a negative value.
For Jerry's rock:
Initial velocity (u2) = 12 m/s (upward)
Final velocity (v2) = ? (at the meeting point)
Time (t) = ? (at the meeting point)
Acceleration (a2) = -9.8 m/s^2 (upward, taking the gravitational acceleration as negative)
Using the same kinematic equation:
v2 = u2 + a2 * t
Since the rocks meet at the same position and time, we can set the displacement (s1) of Heather's rock equal to the displacement (s2) of Jerry's rock.
The displacement formula is given by:
s = u * t + (1/2) * a * t^2
Applying the displacement equation for Heather's rock:
s1 = u1 * t + (1/2) * a1 * t^2
s1 = 12 * t + (1/2) * 9.8 * t^2
Applying the displacement equation for Jerry's rock:
s2 = u2 * t + (1/2) * a2 * t^2
s2 = -12 * t - (1/2) * 9.8 * t^2
Since the rocks meet at the same position, we can set s1 equal to s2:
12 * t + (1/2) * 9.8 * t^2 = -12 * t - (1/2) * 9.8 * t^2
Now, let's solve this equation to find the time (t) when the rocks meet.