Henrietta is going off to her physics class, jogging down the sidewalk at a speed of 4.20 . Her husband Bruce suddenly realizes that she left in such a hurry that she forgot her lunch of bagels, so he runs to the window of their apartment, which is a height 54.2 above the street level and directly above the sidewalk, to throw them to her. Bruce throws them horizontally at a time 8.50 after Henrietta has passed below the window, and she catches them on the run. You can ignore air resistance.With what initial speed must Bruce throw the bagels so Henrietta can catch them just before they hit the ground?Where is Henrietta when she catches the bagels?
Here we have students posting from all over the world, so naturally we use both the metric (m/kg/s) and imperial system (feet/lbs/s).
It is important to post the units to complete the question.
15.5
10
To solve this problem, we can use the principles of projectile motion. We can first find the horizontal distance traveled by Henrietta, and then use that distance to determine where she catches the bagels.
Let's break down the given information:
- Henrietta's speed is 4.20 m/s (meters per second).
- The window is located at a height of 54.2 m above the street.
- Bruce throws the bagels horizontally, 8.50 seconds after Henrietta has passed below the window.
- We need to find Bruce's initial throwing speed and Henrietta's catching position.
To find the horizontal distance traveled by Henrietta, we can use the formula:
distance = speed × time.
In this case, the horizontal distance is simply Henrietta's speed multiplied by the time elapsed since Bruce threw the bagels (8.50 seconds).
distance = 4.20 m/s × 8.50 s = 35.70 meters.
Now that we have the horizontal distance, we can calculate Bruce's initial throwing speed. Since the bagels are thrown horizontally, their vertical velocity component is zero. Therefore, the only motion affecting them is the horizontal motion.
For a horizontally thrown object, the horizontal velocity (Vx) remains constant throughout its motion. The vertical velocity (Vy) is affected by gravity and can be determined using the formula:
Vy = g × t,
where g is the acceleration due to gravity, approximately 9.8 m/s², and t is the time of flight.
Since the vertical velocity is zero when the bagel reaches the ground, we know that the time of flight is the time it takes for the bagels to fall from the window to the ground, which is equal to the time it takes for Henrietta to jog the distance.
To find the time of flight, we can use the formula:
time = distance / speed,
where the distance is the height of the window above the street level (54.2 meters), and the speed is Henrietta's jogging speed (4.20 m/s).
time = 54.2 m / 4.20 m/s = 12.90 seconds.
Now that we have the time of flight, we can find Bruce's initial throwing speed by using the formula:
Vy = g × t.
0 = 9.8 m/s² × 12.90 s.
Therefore, Bruce's initial throwing speed doesn't affect Henrietta catching it before it hits the ground since its vertical velocity is 0.
Henrietta catches the bagels at the horizontal distance of 35.70 meters from the apartment window.