There is more information here than you require to answer the question.
A projectile with initial velocity V that is lauched at an angle A to the horizontal will travel a horizontal distance
X = (2 V^2/g)sin A cos A
= (V^2/g)sin (2A)
Since A = 45 degrees, sin (2A) = 1 and
470 ft = V^2/32.2 ft/s^2
V = 123 ft/s
Use that velocity to calculate how high it will go if launched vertically
gH = V^2/2 (from conservation of energy)
H = V^2/(2g) = X/2 = 235 ft
It can go half as high as it can go horizontally.
A "Stomp Rocket" is a toy projectile launcher illustrated in figure (i) below, which uses a blast of air to propel a dart made of plastic. The air blast is produced by jumping on a plastic bladder as shown in figure (ii) below. It is found that when a 187 lb dad jumps on the bladder, the rocket dart will fly on average a horizontal distance of 470 ft when launched at an angle of 45°.
a).What is the initial velocity of the rocket dart as it leaves the launch tube?
b) If the rocket dart is instead pointed straight up, and the same dad jumps on the launcher, what would be the maximum height obtained?
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