An astronaut on the planet Zircon tosses a rock horizontally with a speed of 6.65 . The rock falls through a vertical distance of 1.50 and lands a horizontal distance of 8.90 from the astronaut.
What is the acceleration of gravity on Zircon?
To calculate the acceleration of gravity on the planet Zircon, we can use the information given about the rock's horizontal and vertical motion.
First, let's break down the information we have:
Initial horizontal velocity (Vx) = 6.65 m/s
Vertical distance (y) = 1.50 m
Horizontal distance (x) = 8.90 m
We can start by calculating the time it takes for the rock to reach the ground vertically. We can use the equation:
y = (1/2) * g * t^2
where y is the vertical distance, g is the acceleration due to gravity, and t is the time.
Plugging in the values we have, we get:
1.50 = (1/2) * g * t^2
Next, let's calculate the time it takes for the rock to travel horizontally:
x = Vx * t
where x is the horizontal distance, Vx is the initial horizontal velocity, and t is the time.
Plugging in the values we have, we get:
8.90 = 6.65 * t
Now, we have two equations with two unknowns (g and t). We can solve these equations simultaneously to find the values.
From the second equation, we can isolate t:
t = 8.90 / 6.65
Now, we substitute this value of t into the first equation:
1.50 = (1/2) * g * (8.90 / 6.65)^2
Simplifying the equation:
1.50 = (1/2) * g * (1.3408506787)^2
Now, we can solve for g by isolating it:
g * (1.3408506787)^2 = 1.50 * 2
g * (1.7937) = 3
g = 3 / 1.7937
Calculating this, we find:
g ≈ 1.6724 m/s²
Therefore, the acceleration of gravity on the planet Zircon is approximately 1.6724 m/s².