Tony Stark tests the limits of his power suit by flying straight upwards. He begins at rest and his net acceleration is \( 2.2 \mathrm{~m} / \mathrm{s}^{2} \) straight up until he runs out of power at 1000 m . We will ignore atmospheric drag. How long did it take him to travel that 1000 m ?

To find the time it took for Tony Stark to travel 1000 m, we can use the equation of motion under constant acceleration: \[ s = ut + \frac{1}{2}at^2 \] where: - \( s \) is the distance traveled (1000 m), - \( u \) is the initial velocity (0 m/s since he starts at rest), - \( a \) is the acceleration (2.2 m/s^2), - \( t \) is the time we are trying to find. Substitute the given values into the equation: \[ 1000 = 0 \times t + \frac{1}{2} \times 2.2 \times t^2 \] Simplify the equation: \[ 1000 = 1.1 \times t^2 \] Now, we can solve for \( t \) by rearranging the equation: \[ t^2 = \frac{1000}{1.1} \] \[ t = \sqrt{\frac{1000}{1.1}} \] Calculate the value of \( t \) to find the time it took for Tony Stark to travel 1000 m. Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{1000}{1.1}}\) - step1: Divide the numbers: \(\sqrt{\frac{10000}{11}}\) - step2: Use the properties of radicals: \(\frac{\sqrt{10000}}{\sqrt{11}}\) - step3: Simplify the expression: \(\frac{100}{\sqrt{11}}\) - step4: Multiply by the Conjugate: \(\frac{100\sqrt{11}}{\sqrt{11}\times \sqrt{11}}\) - step5: Multiply the numbers: \(\frac{100\sqrt{11}}{11}\) The time it took for Tony Stark to travel 1000 m is approximately 30.15 seconds.