If the girl from #1 runs off of the jungle gym into her dad's arms, which are 1m above the ground, how fast is she moving just before she's caught by her dad?
To determine the girl's speed just before she is caught by her dad, we need to know the initial height from which she jumps, as well as the time it takes for her to reach her dad's arms. Without this information, we cannot directly calculate her speed.
However, we can estimate the girl's speed using the principles of physics. We will make a few assumptions for this estimation:
1. We assume that the girl starts from rest, which means she has no initial velocity when she jumps.
2. We will ignore air resistance, assuming it is negligible.
3. We will consider only the vertical motion of the girl.
Now, using the laws of physics, we can calculate the girl's speed just before being caught by her dad by using the equation of motion for free fall:
𝑣² = 𝑢² + 2đť‘Žđť‘
Where:
- đť‘Ł is the final velocity (speed) of the girl just before being caught by her dad
- 𝑢 is the initial velocity (which is zero in this case)
- 𝑎 is the acceleration due to gravity (approximately 9.8 m/s²)
- đť‘ is the displacement, which is the distance the girl falls (which we need to determine)
To find the displacement đť‘ , we need to know the initial height from which the girl jumps. If the initial height is known, we can find the displacement using the equation:
𝑠= 𝑢𝑡 + 0.5𝑎𝑡²
Where:
- 𝑡 is the time it takes for the girl to reach her dad's arms (which we still need to determine)
Once we have calculated the displacement, we can substitute the values into the first equation to find the girl's final velocity just before being caught by her dad.