Isaac is standing on a ladder picking apples in his grandfather’s orchard. As he pulls each apple off the tree, he tosses it into a basket that sits on the ground 2.1 m down and 3.6 m away horizontally. How fast must Isaac throw the apples (horizontally) to land them in the basket?
To calculate the required velocity at which Isaac should throw the apples horizontally in order to land them in the basket, we can make use of projectile motion equations.
Let's consider the horizontal distance, which is 3.6 m. The only force acting on the apple in the horizontal direction is the initial velocity given by Isaac's throw. There is no acceleration or external force along this direction.
We can start by using the horizontal motion equation:
distance = velocity * time
In this case, the distance is 3.6 m, and we are trying to find the velocity. Time is not given, but we can determine it by considering the vertical motion of the apple.
The vertical motion of the apple is influenced by the acceleration due to gravity (9.8 m/s²). Initially, the apple is at a height of 2.1 m and its final position is at the ground (height = 0). We can use the vertical motion equation:
distance = initial velocity * time + (1/2) * acceleration * time²
In this case, the distance is 2.1 m, the initial velocity is 0 m/s (since Isaac throws the apple horizontally), and the acceleration is -9.8 m/s² (negative because it acts downward).
By substituting these values into the equation, we get:
2.1 = 0 * time + (1/2) * (-9.8) * time²
Simplifying the equation, we have:
2.1 = (-4.9) * time²
Dividing both sides by (-4.9), we get:
time² = -2.1/-4.9
time² ≈ 0.4286
Taking the square root of both sides, we obtain:
time ≈ √0.4286
time ≈ 0.654 s
Now that we know the time it takes for the apple to fall to the ground, we can go back to the horizontal motion equation:
3.6 = velocity * 0.654
Solving for velocity:
velocity = 3.6 / 0.654
velocity ≈ 5.50 m/s
Therefore, Isaac must throw the apples horizontally at a speed of approximately 5.50 m/s to land them in the basket.
how long does it take to fall 2.1m?
4.9t^2 = 2.1
Now, with that t, find v using
vt = 3.6