Superman is standing 393 m horizontally away from Lois Lane. A villain drops a rock from 4.00 m directly above Lois. If Superman is to intervene and catch the rock just before it hits Lois, what should be his minimum constant acceleration? If the acceleration is toward Lois, enter a positive value. If the acceleration is away from Lois, enter a negative value.

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 4=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{4\times 2}{9.81}}\\\Rightarrow t=0.903\ s[/tex]

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 393=0\times 0.0903+\frac{1}{2}\times a\times 0.903^2\\\Rightarrow a=\frac{393\times 2}{0.903^2}\\\Rightarrow a=963.93\ m/s^2[/tex]

The acceleration of Superman would be -963.93 m/s² from Lois' perspective

Abdulazeez10 Abdulazeez10 · Answer 2 · 2022-04-12T12:08:45+02:00

The Superman minimum constant acceleration should be 963 m/s²

Linear motion and free falling bodies

From the question, we are to determine what the mininum acceleration of the Superman should be

First, we will determine how long it will take the rock to hit Lois.

Height from which the rock was dropped = 4.00m

Since the rock was dropped, the initial velocity is 0 m/s

From one of the equations for free falling bodies, we have

[tex]h = ut + \frac{1}{2} gt^{2}[/tex]

Where h is the height

u is the initial velocity

t is the time taken

and g is the acceleration due to gravity (g = 9.8 m/s²)

Putting the parameters into the equation, we get

[tex]4.00 = 0(t) + \frac{1}{2}(9.8)t^{2}[/tex]

[tex]4.00 = 4.9t^{2}[/tex]

[tex]t^{2} = \frac{4.00}{4.9}[/tex]

[tex]t = \sqrt{\frac{4.00}{4.9} }[/tex]

[tex]t = 0.9035 \ sec[/tex]

This means it will take 0.9035 sec for the rock to hit Lois.

From the given information,

The distance the Superman would have to cover is 393 m

And he needs to get there in less than 0.9035 sec

From one the equations for linear motion,

[tex]S = ut + \frac{1}{2} at^{2}[/tex]

Where S is the distance

u is the initial velocity

t is the time taken

and a is the acceleration

Then,

S = 393 m

t = 0.9035 sec

u = 0 m/s (Since the Superman will start from rest)

Putting the parameters into the equation,

[tex]S = ut + \frac{1}{2} at^{2}[/tex]

Recall from above that,

[tex]t^{2} = \frac{4.00}{4.9}[/tex]

Then,

[tex]393= (0)(0.9035) + \frac{1}{2}\times a\times \frac{4.00}{4.9}[/tex]

[tex]393= a\times \frac{2.00}{4.9}[/tex]

[tex]a = \frac{393 \times 4.9}{2.00}[/tex]

[tex]a = 962.85 \ m/s^{2}[/tex]

[tex]a \approx 963 \ m/s^{2}[/tex]

Hence, the Superman minimum constant acceleration should be 963 m/s²

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