You kick a soccer ball from ground level with an initial velocity of 7.80 m/s at

Question

You kick a soccer ball from ground level with an initial velocity of 7.80 m/s at an angle of 30.0° above the horizontal. When the ball strikes a wall that is some distance from you the ball is 39.0 cm off the ground. You want to determine how far away the wall is. Use g = 9.80 m/s2.

(a) Based on the information above, how many possible answers are there for the distance from you to the wall, assuming that the ball does not bounce before hitting the wall and assuming air resistance can be neglected?

(b) Find the largest of these distances.

I got part a right (the answer is 2) but I guessed and I don't know why the answer is 2. And I keep getting part b wrong. Please help and show how to do it :(

Explanation / Answer

here,

initial velocity of the ball , u = 7.8 m/s

theta = 30 degree

height of the wall , h = 39 cm

h = 0.39 m

equation of trajectory , y = x * tan(theta) - g*x^2/(2 * v^2 * cos^2(theta))

let the horizontal distance of wall be x

therefore,

0.39 = x * tan(30) - 9.8 * x^2/(2 * 7.8^2 * cos^2(30))

x = 0.79 m

x = 4.58 m

there are two possible answers

(b)

the largest of these distance is 4.58 m

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