An 80- quarterback jumps straight up in the air right before throwing a 0.43- football horizontally at 15 . How fast will he be moving backward just after releasing the ball? Suppose that the quarterback takes 0.30 to return to the ground after throwing the ball. How far d will he move horizontally, assuming his speed is constant?
2.4*10^-2 m
I think just giving the person an answer is a little unhelpful.
m(Vf-Vi)=m(Vf-Vi)
80(Vf-0)=0.43(15-0)
80(Vf)=0.43(15)
80(Vf)=6.45
Vf=0.80625 m/s
0.080625 m/s * 0.03 m = 0.0241875 m the QB moves horizontally.
where did that 0.03 come from lol.
Well, let's break this down, shall we?
First, I have to ask, why is the quarterback jumping? Did he see a spider on the ground? Or maybe he's auditioning for a role in a sports-themed ballet? Regardless, it's important to note that his vertical motion doesn't affect his horizontal velocity.
Now, to find out how fast the quarterback will be moving backward just after releasing the ball, we need to consider the horizontal velocity of the ball. Given that the football was thrown horizontally at 15 meters per second, the quarterback will also be moving backward at the same speed. So, he'll be zipping through the air at a brisk 15 meters per second in reverse. Time to break out those driving skills!
Next, let's talk about how far the quarterback will move horizontally assuming his speed is constant. Since we know that the quarterback takes 0.30 seconds to return to the ground after throwing the ball, we can use that time to calculate the distance traveled horizontally. Now, assuming he throws the ball while in the air, his horizontal velocity will remain constant. So, we can use the formula distance = velocity × time.
Using a velocity of 15 meters per second and a time of 0.30 seconds, we find that the quarterback will move backward by a distance of 4.5 meters. That's like taking two steps back, but with style!
Hope that clears things up for you!
To find the speed at which the quarterback will be moving backward just after releasing the ball, we can use the concept of conservation of momentum.
1. Calculate the momentum of the football before it is thrown:
- Mass of the football (m1) = 0.43 kg
- Velocity of the football (v1) = 15 m/s (horizontal)
- Momentum of the football before it is thrown (p1) = m1 * v1
2. Calculate the momentum of the quarterback just after releasing the ball:
- Mass of the quarterback (m2) = 80 kg
- Velocity of the quarterback just after releasing the ball (v2) = ?
- Momentum of the quarterback just after releasing the ball (p2) = m2 * v2
According to the conservation of momentum, the total momentum before and after the ball is thrown should be the same:
p1 = p2
m1 * v1 = m2 * v2
0.43 kg * 15 m/s = 80 kg * v2
6.45 kg·m/s = 80 kg * v2
Now, we can solve for v2 (velocity of the quarterback just after releasing the ball):
v2 = 6.45 kg·m/s / 80 kg
v2 = 0.080625 m/s
Therefore, the quarterback will be moving backward at a speed of 0.0806 m/s just after releasing the ball.
To calculate how far the quarterback will move horizontally assuming his speed is constant:
3. Use the formula for distance (d = v * t):
- Velocity of the quarterback (v) = 0.0806 m/s (backward velocity)
- Time taken for the quarterback to return to the ground (t) = 0.30 s
d = v * t
d = 0.0806 m/s * 0.30 s
d = 0.0242 meters
Therefore, the quarterback will move approximately 0.0242 meters horizontally.