Think of a projectile motion on an inclined table with the inclination angle α=6.The elevation angle is θ=30 and V0 is 40 cm/s. What is the percentage error (approximately) in hmax if the measured value of hmax is 5 cm? (sin6=0.1, g=10 m/s2)
To find the percentage error in hmax, we need to compare the measured value with the actual value.
First, let's find the actual value of hmax using the given information.
In projectile motion, the maximum height (hmax) can be found using the formula:
hmax = (V0^2 * sin^2(θ)) / (2 * g)
Given:
V0 = 40 cm/s
sin(θ) = 0.5 (since θ = 30 degrees)
g = 10 m/s^2
Let's convert V0 from cm/s to m/s:
V0 = 40 cm/s = 0.4 m/s
Now, substitute the values into the formula:
hmax = (0.4^2 * sin^2(30)) / (2 * 10)
hmax = (0.16 * 0.25) / 20
hmax = 0.004 / 20
hmax = 0.0002 m
Now, we can find the percentage error using the formula:
Percentage Error = | (measured value - actual value) / actual value | * 100
Substitute the measured value (5 cm = 0.05 m) and the actual value we calculated (0.0002 m) into the formula:
Percentage Error = | (0.05 - 0.0002) / 0.0002 | * 100
Percentage Error = | 0.0498 / 0.0002 | * 100
Percentage Error = 249 * 100
Percentage Error ≈ 24,900%
So, the percentage error in hmax is approximately 24,900%.