To find the potential difference between the starting point and the top point of the trajectory on planet Tehar, you can use the following steps:
1. Calculate the time it takes for the ball to reach the top of its trajectory.
2. Determine the maximum height reached by the ball.
3. Calculate the change in electric potential energy.
Let's go through each step:
Step 1: Calculate the time to reach the top of the trajectory.
We know the ball hits the ground after 4.10 seconds, so the time to reach the top is half of that time:
Time to reach the top = 4.10 s / 2 = 2.05 s
Step 2: Calculate the maximum height reached by the ball.
You can use the kinematic equation:
\[h = \frac{1}{2}gt^2\]
where
h = maximum height
g = acceleration due to gravity (same as Earth, approximately 9.81 m/s² on Tehar)
t = time to reach the top (2.05 s)
\[h = \frac{1}{2} \cdot 9.81 \, \text{m/s²} \cdot (2.05 \, \text{s})^2\]
\[h \approx 20.25 \, \text{m}\]
Step 3: Calculate the change in electric potential energy.
The change in electric potential energy (ΔPE) is equal to the work done by the electric field, which is the product of the electric field strength (E) and the charge (q):
\[ΔPE = Eq\]
Given that the charge q = 4.98 µC (microCoulombs) and there is a strong downward electric field, the electric field strength is negative. We need to convert the charge to Coulombs:
\[q = 4.98 \times 10^{-6} \, \text{C}\]
Now, you need to find the electric field strength. Since the electric field is uniform, it can be calculated using the formula:
\[E = \frac{F}{q}\]
The force (F) is the weight of the ball, which is equal to its mass (m) times the acceleration due to gravity (g):
\[F = mg\]
Plug in the values:
\[F = (1.98 \, \text{kg}) \cdot (9.81 \, \text{m/s²})\]
Calculate F and then use it to find the electric field strength (E). Once you have E, you can calculate ΔPE:
\[ΔPE = Eq\]
Finally, the potential difference (V) is equal to the change in electric potential energy divided by the charge:
\[V = \frac{ΔPE}{q}\]
Calculate V using the values you've found, and you'll have the potential difference between the starting point and the top point of the trajectory on planet Tehar.