Bert is standing on a ladder picking apples in his father's orchard. As he pulls each apple off the tree, he tosses it into a basket that sits on the ground 2.5 m below at a horizontal distance of 1.9 m from Bert. How fast must Bert throw the apples (horizontally) in order for them to land in the basket? Enter m/s as unit and use g = 10. m/s2.

Question

Bert is standing on a ladder picking apples in his father's orchard. As he pulls each apple off the tree, he tosses it into a basket that sits on the ground 2.5 m below at a horizontal distance of 1.9 m from Bert. How fast must Bert throw the apples (horizontally) in order for them to land in the basket? Enter m/s as unit and use g = 10. m/s2.

Answer 1

Calculate how long it takes the apple to fall 2.5 m. Then divide 1.9 meters (the horizontal distance) by that time.

That will give you the required throwing speed.

Answer 2

To determine the horizontal velocity at which Bert must throw the apples for them to land in the basket, we can use the equation for projectile motion.

In this case, the horizontal distance (range) and vertical distance (height) are known. The horizontal distance is given as 1.9 m, and the vertical distance is 2.5 m.

Let's assume that Bert throws the apples with an initial horizontal velocity of v_x (m/s) and initial vertical velocity of v_y (m/s). Since there are no external horizontal forces acting on the apple after it is thrown, the horizontal velocity remains constant throughout its flight. This means that v_x is also the horizontal velocity at the moment the apple reaches the basket.

Using the equations of projectile motion, we have:

1. Vertical motion equation:
h = v_y * t - (1/2) * g * t^2
where h is the vertical distance (2.5 m), v_y is the initial vertical velocity, g is the acceleration due to gravity (10 m/s^2), and t is the time of flight.

2. Horizontal motion equation:
s = v_x * t
where s is the horizontal distance (1.9 m).

To find the time of flight (t), we can rearrange equation 1 to solve for t:
t = (v_y ± sqrt(v_y^2 + 2 * g * h)) / g
Since the apple is initially thrown horizontally, v_y = 0, and we can simplify the equation to:
t = sqrt(2 * h / g)

Now we can substitute the value of t into equation 2 to solve for v_x:
s = v_x * sqrt(2 * h / g)
Rearranging for v_x, we get:
v_x = s / sqrt(2 * h / g)

Substituting the given values, we have:
v_x = 1.9 / sqrt(2 * 2.5 / 10)

Simplifying further, we get:
v_x = 1.9 / sqrt(1)

Thus, the horizontal velocity at which Bert must throw the apples for them to land in the basket is equal to 1.9 m/s.

Calculate how long it takes the apple to fall 2.5 m. Then divide 1.9 meters (the horizontal distance) by that time.

1m/s

To determine the horizontal velocity at which Bert must throw the apples for them to land in the basket, we can use the equation for projectile motion.