To determine if Jack burned his feet on the .25 m high candle, we can use the equation for projectile motion: h = h0 + (v0sinθ)t - (1/2)gt^2. In this case, h0 = 0 (since Jack starts at ground level), v0 = 5 m/s, θ = 30 degrees, g = 9.8 m/s^2 (acceleration due to gravity), and t is the time it takes for Jack to reach the candle.
We can solve for t by setting h = 0.25 m (height of the candle) and solving for t. Plugging in the values, we get:
0.25 = 0 + (5sin30)t - (1/2)(9.8)t^2
0.25 = (2.5)t - (4.9)t^2
0 = (4.9)t^2 - (2.5)t + 0.25
Using the quadratic formula, we can solve for t and get two solutions: t = 0.1 s or t = 0.05 s. Since the time cannot be negative, we can disregard the negative solution and conclude that it took Jack approximately 0.1 seconds to reach the candle.
Now, we can plug this value of t into the equation for horizontal displacement: x = x0 + (v0cosθ)t. In this case, x0 = 0 (since Jack starts at ground level), v0 = 5 m/s, and θ = 30 degrees. Plugging in the values, we get:
x = 0 + (5cos30)(0.1)
x = 0 + (5)(√3/2)(0.1)
x = 0 + 2.5(0.1)
x = 0.25 m
This means that Jack's horizontal displacement (or how far he traveled horizontally) is 0.25 meters, which is equal to the height of the candle. Therefore, Jack did not burn his feet on the .25 m high candle as he jumped over it with just enough clearance.
