while standing on an open truck moving at a velocity of 35m/s, a man sees a duck flying diresctly overhead. The man shoots an arrow at the duck and misses it.. the arrow leaves the bow at a vertical velocity of 98m/s. the truck accelerates to a constant speed of 40m/s in the same direction just after the man has shot at the duck. If the truck open board at which the man is standing is 2m above the ground.
1)how long will the arrow remain in air before hitting the ground
2)where will the arrow land in relation to the position of the truck
I20
To answer these questions, we need to break down the problem into two parts: the horizontal motion and the vertical motion of the arrow. Let's analyze each part separately.
1) Horizontal Motion:
Since the truck is moving at a constant velocity and the arrow leaves the bow with a vertical velocity, we can assume that the horizontal component of the arrow's motion is not affected by the truck's movement. Therefore, we can ignore the truck's velocity for this part of the problem.
2) Vertical Motion:
Let's analyze the vertical motion of the arrow. We have the initial vertical velocity (98 m/s) and the height of the truck (2 m). The arrow will continue to accelerate due to gravity (-9.8 m/s^2), as it would if it were not shot from a moving platform.
We can use the kinematic equation to determine the time it takes for the arrow to hit the ground. The formula is given by:
h = vi * t + (1/2) * g * t^2
Where:
- h is the displacement in the vertical direction (in this case, the height of the truck).
- vi is the initial vertical velocity.
- g is the acceleration due to gravity.
- t is the time it takes for the arrow to reach the ground.
Plugging in the values, we have:
2 m = 98 m/s * t + (1/2) * -9.8 m/s^2 * t^2
This is a quadratic equation. Solving it will give us the value of time (t) when the arrow hits the ground.
Now, let's move on to question 2:
To determine where the arrow lands in relation to the position of the truck, we need to consider the horizontal motion of the arrow. Since the arrow was shot straight up, its horizontal velocity remains constant. This is because the only external force acting on the arrow is gravity, which does not affect its horizontal motion.
Therefore, we can use the formula:
d = v * t
Where:
- d is the horizontal distance traveled by the arrow.
- v is the horizontal velocity.
- t is the time calculated from question 1.
Plugging in the values, we have:
d = 35 m/s * t
This will give us the horizontal distance traveled by the arrow.
Remember to solve question 1 first to get the value of time (t), and then use that value to solve question 2.